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| {{Infobox scientist
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| |name = John R. Stallings
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| |image = Stallings.jpg
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| |caption = 2006 photo of Stallings
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| |birth_date = {{Birth date|1935|7|22}}
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| |birth_place = [[Morrilton, Arkansas]], [[United States]]
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| |death_date = {{death date and age|2008|11|24|1935|7|22}}
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| |death_place = [[Berkeley, California]], [[United States]]
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| |residence =
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| |nationality = [[United States]]
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| |field = [[Mathematics]]
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| |work_institutions = [[University of California at Berkeley]]
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| |alma_mater = [[University of Arkansas]]<br>[[Princeton University]]
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| |doctoral_advisor = [[Ralph Fox]]
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| |doctoral_students =
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| |known_for = proof of [[Generalized Poincaré conjecture|Poincaré Conjecture in dimensions greater than six]]; [[Stallings theorem about ends of groups]]
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| |prizes = [[Cole Prize|Frank Nelson Cole Prize in Algebra]] (1971)
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| |Erdős number =
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| |religion =
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| |footnotes =
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| }}
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| '''John Robert Stallings Jr.''' (July 22, 1935 – November 24, 2008) was a [[mathematician]] known for his seminal contributions to [[geometric group theory]] and [[Low-dimensional topology|3-manifold topology]]. Stallings was a Professor Emeritus in the Department of Mathematics at the [[University of California at Berkeley]]<ref name="UCBPR">[http://berkeley.edu/news/media/releases/2009/01/12_stallings.shtml Mathematician John Stallings died last year at 73.] [[UC Berkeley]] press release, January 12, 2009. Accessed January 26, 2009</ref> where he had been a faculty member since 1967.<ref name="UCBPR"/> He published over 50 papers, predominantly in the areas of [[geometric group theory]] and the topology of [[3-manifold]]s. Stallings' most important contributions include a proof, in a 1960 paper, of the [[Generalized Poincaré conjecture|Poincaré Conjecture in dimensions greater than six]] and a proof, in a 1971 paper, of the [[Stallings theorem about ends of groups]].
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| ==Biographical data==
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| John Stallings was born on July 22, 1935 in [[Morrilton, Arkansas]].<ref name="UCBPR"/>
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| Stallings received his B.Sc. from [[University of Arkansas]] in 1956 (where he was one of the first two graduates in the university's Honors program)<ref>[http://libinfo.uark.edu/ata/v3no4/honorscollege.asp All things academic.] Volume 3, Issue 4; November 2002.</ref> and he received a Ph.D. in Mathematics from [[Princeton University]] in 1959 under the direction of [[Ralph Fox]].<ref name="UCBPR"/>
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| After completing his PhD, Stallings held a number of postdoctoral and faculty positions, including being an NSF postdoctoral fellow at [[Oxford University]] as well as and instructorship and a faculty appointment at Princeton. Stallings joined the University of California at Berkeley as a faculty member in 1967 where he remained until his retirement in 1994.<ref name="UCBPR"/> Even after his retirement, Stallings continued supervising UC Berkeley graduate students until 2005.<ref name="NYT"/> Stallings was an [[Sloan Fellowship|Alfred P. Sloan Research fellow]] from 1962–65 and a Miller Institute fellow from 1972-73.<ref name="UCBPR"/>
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| Over the course of his career, Stallings had 22 doctoral students including [[Marc Culler]] and [[J. Hyam Rubinstein|Hyam Rubinstein]] and 60 doctoral descendants. He published over 50 papers, predominantly in the areas of [[geometric group theory]] and the topology of [[3-manifold]]s.
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| Stallings delivered an invited address as the [[International Congress of Mathematicians]] in [[Nice]] in 1970<ref>John R. Stallings. ''Group theory and 3-manifolds.'' Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, pp. 165–167. Gauthier-Villars, Paris, 1971.</ref> and a James K. Whittemore Lecture at [[Yale University]] in 1969.<ref name="SWM">John Stallings. ''Group theory and three-dimensional manifolds.''
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| A James K. Whittemore Lecture in Mathematics given at Yale University, 1969. Yale Mathematical Monographs, 4. [[Yale University Press]], New Haven, Conn.–London, 1971.</ref>
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| Stallings received the [[Cole Prize|Frank Nelson Cole Prize in Algebra]] from the [[American Mathematical Society]] in 1970.<ref>[http://www.ams.org/prizes/cole-prize-algebra.html Frank Nelson Cole Prize in Algebra.] [[American Mathematical Society]].</ref>
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| The conference "Geometric and Topological Aspects of Group Theory", held at the [[Mathematical Sciences Research Institute]] in Berkeley in May 2000, was dedicated to the 65th birthday of Stallings.<ref>[http://atlas-conferences.com/cgi-bin/calendar/d/faam71 Geometric and Topological Aspects of Group Theory, conference announcement], atlas-conferences.com</ref>
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| In 2002 a special issue of the journal [[Geometriae Dedicata]] was dedicated to Stallings on the occasion of his 65th birthday.<ref>[http://www.springerlink.com/content/acnlhf5dylu1/?p=36fc0e096ab34a99bf226a2b5cd5ca0a&pi=0 Geometriae Dedicata], vol. 92 (2002). Special issue dedicated to John Stallings on the occasion of his 65th birthday. Edited by R. Z. Zimmer.</ref> Stallings died from [[prostate cancer]] on November 24, 2008.<ref name="NYT">{{citation|title=John R. Stallings Jr., 73, California Mathematician, Is Dead|journal=[[New York Times]]|date=January 18, 2009|url=http://www.nytimes.com/2009/01/19/us/19stallings.html|first=Kenneth|last=Chang}}. Accessed January 26, 2009.</ref><ref>[http://math.berkeley.edu/home.html Professor Emeritus John Stallings of the UC Berkeley Mathematics Department has died.] Announcement at the website of the Department of Mathematics of the [[University of California at Berkeley]]. Accessed December 4, 2008</ref>
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| ==Mathematical contributions==
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| Most of Stallings' mathematical contributions are in the areas of [[geometric group theory]] and [[low-dimensional topology]] (particularly the topology of [[3-manifold]]s) and on the interplay between these two areas.
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| An early significant result of Stallings is his 1960 proof<ref>John Stallings. [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183523757 ''Polyhedral homotopy spheres.''] [[Bulletin of the American Mathematical Society]], vol. 66 (1960), pp. 485–488.</ref> of the [[Generalized Poincaré conjecture|Poincaré Conjecture in dimensions greater than six]]. (Stallings' proof was obtained independently from and shortly after the different proof of [[Steve Smale]] who established the same result in dimensions bigger than four<ref>S. Smale. ''Generalized Poincaré's conjecture in dimensions greater than four''. [[Annals of Mathematics]] (2nd Ser.), vol. 74 (1961), no. 2, pp. 391–406</ref>).
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| Using "engulfing" methods similar to those in his proof of the Poincaré Conjecture for ''n'' > 6, Stallings proved that ordinary Euclidean ''n''-dimensional space has a unique piecewise linear, hence also smooth, structure, if ''n'' is not equal to 4. This took on added significance when, as a consequence of work of [[Michael Freedman]] and [[Simon Donaldson]] in 1982, it was shown that 4-space has [[exotic R4|exotic smooth structures]], in fact uncountably many such.
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| In a 1963 paper<ref>John Stallings.
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| ''A finitely presented group whose 3-dimensional integral homology is not finitely generated.''
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| [[American Journal of Mathematics]], vol. 85 (1963), pp. 541–543</ref> Stallings constructed an example of a [[finitely presented group]] with infinitely generated 3-dimensional integral [[Group homology|homology group]] and, moreover, not of the type <math>\mathcal F_3 </math>, that is, not admitting a [[classifying space]] with a finite 3-skeleton. This example came to be called the ''Stallings group'' and is a key example in the study of homological finiteness properties of groups. Bieri later showed<ref>Robert Bieri. ''Homological dimension of discrete groups.''
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| Queen Mary College Mathematical Notes. [[Queen Mary, University of London|Queen Mary College]], Department of Pure Mathematics, London, 1976.</ref> that the Stallings group is exactly the kernel of the homomorphism from the direct product of three copies of the [[free group]] ''F''<sub>2</sub> to the additive group '''Z''' of integers that sends to 1 ∈ '''Z''' the six elements coming from the choice of free bases for the three copies of ''F''<sub>2</sub>. Bieri also showed that the Stallings group fits into a sequence of examples of groups of type <math>\mathcal F_n </math> but not of type <math>\mathcal F_{n+1} </math>. The Stallings group is a key object in the version of discrete [[Morse theory]] for cubical complexes developed by [[Mladen Bestvina|Bestvina]] and Brady<ref>Mladen Bestvina, and Noel Brady. [http://www.springerlink.com/content/nhj24dgb0vb7bx5p/?p=62f8c742e1c64076994f8b151392c1f6&pi=1 ''Morse theory and finiteness properties of groups''.] [[Inventiones Mathematicae]], vol. 129 (1997), no. 3, pp. 445–470</ref> and in the study of subgroups of direct products of [[limit group]]s.<ref>Martin R. Bridson, James Howie, Charles F. Miller, and Hamish Short. [http://www.springerlink.com/content/l7653623q4205434/ ''The subgroups of direct products of surface groups''.] [[Geometriae Dedicata]], vol. 92 (2002), pp. 95–103.</ref><ref>Martin R. Bridson, and James Howie. [http://www.springerlink.com/content/w34016g8379x5q47/ ''Subgroups of direct products of elementarily free groups.''] [[Geometric and Functional Analysis]], vol. 17 (2007), no. 2, pp. 385–403</ref><ref>Martin R. Bridson, and James Howie. [http://www.mrlonline.org/mrl/2007-014-004/2007-014-004-001.pdf ''Subgroups of direct products of two limit groups.''] Mathematical Research Letters, vol. 14 (2007), no. 4, 547–558</ref>
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| Stallings' most famous theorem in [[group theory]] is an algebraic characterization of groups with more than one [[End (topology)|end]] (that is, with more than one "connected component at infinity"), which is now known as [[Stallings theorem about ends of groups|Stallings' theorem about ends of groups]]. Stallings proved that a [[finitely generated group]] ''G'' has more than one end if and only if this group admits a nontrivial splitting as an [[free product with amalgamation|amalgamated free product]] or as an [[HNN-extension]] over a finite group (that is, in terms of [[Bass-Serre theory]], if and only if the group admits a nontrivial action on a [[tree (graph theory)|tree]] with finite edge stabilizers). More precisely, the theorem states that a [[finitely generated group]] ''G'' has more than one end if and only if either ''G'' admits a splitting as an [[free product with amalgamation|amalgamated free product]] <math>\scriptstyle G=A\ast_C B</math>, where the group ''C'' is finite and ''C'' ≠ ''A'', ''C'' ≠ ''B'', or ''G'' admits a splitting as an [[HNN-extension]] <math>\scriptstyle G=\langle H, t | t^{-1}Kt=L\rangle</math> where ''K'',''L'' ≤ ''H'' are finite [[subgroup]]s of ''H''.
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| Stallings proved this result in a series of works, first dealing with the torsion-free case (that is, a group with no nontrivial elements of finite [[Order (group theory)|order]])<ref>John R. Stallings. ''On torsion-free groups with infinitely many ends.'' [[Annals of Mathematics]] (2), vol. 88 (1968), pp. 312–334.</ref> and then with the general case.<ref name="SWM"/><ref>John Stallings. ''Groups of cohomological dimension one.'' Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVIII, New York, 1968) pp. 124–128. [[American Mathematical Society]], Providence, R.I, 1970.</ref> Stalling's theorem yielded a positive solution to the long-standing open problem about characterizing finitely generated groups of cohomological dimension one as exactly the [[free group]]s.<ref>John R. Stallings. [http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.bams/1183529548&page=record ''Groups of dimension 1 are locally free.''] Bulletin of the American Mathematical Society, vol. 74 (1968), pp. 361–364</ref> Stallings' theorem about ends of groups is considered one of the first results in [[geometric group theory]] proper since it connects a geometric property of a group (having more than one end) with its algebraic structure (admitting a splitting over a finite subgroup). Stallings' theorem spawned many subsequent alternative proofs by other mathematicians (e.g.<ref>M. J.Dunwoody. [http://www.springerlink.com/content/yp22n46n40813lwr/ ''Cutting up graphs.''] Combinatorica 2 (1982), no. 1, pp. 15–23.</ref><ref>Warren Dicks, and M. J. Dunwoody. [http://books.google.com/books?id=xgsM5BvkMvIC&printsec=frontcover&dq=Warren+Dicks,+and+M.+J.+Dunwoody.+Groups+acting+on+graphs ''Groups acting on graphs.''] Cambridge Studies in Advanced Mathematics, 17. [[Cambridge University Press]], Cambridge, 1989. ISBN 0-521-23033-0</ref>) as well as many applications (e.g.<ref>Peter Scott. [http://www.jstor.org/pss/2374238 ''A new proof of the annulus and torus theorems.''] American Journal of Mathematics, vol. 102 (1980), no. 2, pp. 241–277</ref>). The theorem also motivated several generalizations and relative versions of Stallings' result to other contexts, such as the study of the notion of relative ends of a group with respect to a subgroup,<ref>G. A.Swarup. [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0K-45FT7S1-2F&_user=571676&_coverDate=12%2F31%2F1977&_rdoc=11&_fmt=high&_orig=browse&_srch=doc-info(%23toc%235649%231977%23999889998%23298178%23FLP%23display%23Volume)&_cdi=5649&_sort=d&_docanchor=&_ct=28&_acct=C000029040&_version=1&_urlVersion=0&_userid=571676&md5=96e9b99d8411df349be7999d21503ca9 ''Relative version of a theorem of Stallings.'']
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| Journal of Pure and Applied Algebra, vol. 11 (1977/78), no. 1–3, pp. 75–82</ref><ref>M. J. Dunwoody, and E. L. Swenson. [http://www.springerlink.com/content/892hyejtew7h2vg5/ ''The algebraic torus theorem.''] [[Inventiones Mathematicae]], vol. 140 (2000), no. 3, pp. 605–637</ref><ref>G. P. Scott, and G. A. Swarup. [http://nyjm.albany.edu:8000/PacJ/p/2000/196-2-13.pdf ''An algebraic annulus theorem.''] Pacific Journal of Mathematics, vol. 196 (2000), no. 2, pp. 461–506</ref> including a connection to [[CAT(0) space|CAT(0) cubical complexes]].<ref>Michah Sageev. [http://plms.oxfordjournals.org/cgi/content/abstract/s3-71/3/585 ''Ends of group pairs and non-positively curved cube complexes.''] [[Proceedings of the London Mathematical Society]] (3), vol. 71 (1995), no. 3, pp. 585–617</ref> A comprehensive survey discussing, in particular, numerous applications and generalizations of Stallings' theorem, is given in a 2003 paper of [[Terry Wall|Wall]].<ref>C. T. Wall. ''The geometry of abstract groups and their splittings.''
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| Revista Matemática Complutense vol. 16 (2003), no. 1, pp. 5–101.</ref>
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| Another influential paper of Stalling is his 1983 article "Topology on finite graphs".<ref>John R. Stallings. [http://www.springerlink.com/content/mn2h645qw2058530/ ''Topology of finite graphs.''] [[Inventiones Mathematicae]], vol. 71 (1983), no. 3, pp. 551–565</ref> Traditionally, the algebraic structure of [[subgroup]]s of [[free group]]s has been studied in [[combinatorial group theory]] using combinatorial methods, such as the [[Schreier's subgroup lemma|Schreier rewriting method]] and [[Nielsen transformation]]s.<ref>[[Roger Lyndon|Roger C. Lyndon]] and Paul E. Schupp. [http://books.google.com/books?id=aiPVBygHi_oC&printsec=frontcover&dq=Roger+C.+Lyndon+and+Paul+E.+Schupp.+Combinatorial+Group+Theory ''Combinatorial Group Theory.''] Springer–Verlag, New York, 2001. "Classics in Mathematics" series, reprint of the 1977 edition. ISBN 978-3-540-41158-1</ref> Stallings' paper put forward a topological approach based on the methods of [[covering space|covering space theory]] that also used a simple [[graph theory|graph-theoretic]] framework. The paper introduced the notion of what is now commonly referred to as ''Stallings subgroup graph'' for describing subgroups of free groups, and also introduced a foldings technique (used for approximating and algorithmically obtaining the subgroup graphs) and the notion of what is now known as a ''Stallings folding''. Most classical results regarding subgroups of free groups acquired simple and straightforward proofs in this set-up and Stallings' method has become the standard tool in the theory for studying the subgroup structure of free groups, including both the algebraic and algorithmic questions (see <ref name="KWM">Ilya Kapovich, and Alexei Myasnikov. ''Stallings foldings and subgroups of free groups.'' [[Journal of Algebra]], vol. 248 (2002), no. 2, 608–668</ref>). In particular, Stallings subgroup graphs and Stallings foldings have been the used as a key tools in many attempts to approach the [[Hanna Neumann conjecture]].<ref>J. Meakin, and P. Weil. ''Subgroups of free groups: a contribution to the Hanna Neumann conjecture.''
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| Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part I (Haifa, 2000).
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| Geometriae Dedicata, vol. 94 (2002), pp. 33–43.</ref><ref>Warren Dicks. ''Equivalence of the strengthened Hanna Neumann conjecture and the amalgamated graph conjecture.'' [[Inventiones Mathematicae]], vol. 117 (1994), no. 3, pp. 373–389.</ref><ref>Warren Dicks, and [[Edward Formanek]]. ''The rank three case of the Hanna Neumann conjecture''. Journal of Group Theory, vol. 4 (2001), no. 2, pp. 113–151</ref><ref>Bilal Khan. ''Positively generated subgroups of free groups and the Hanna Neumann conjecture.'' Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), pp. 155–170, Contemp. Math., 296, Amer. Math. Soc., Providence, RI, 2002; ISBN 0-8218-2822-3</ref>
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| Stallings subgroup graphs can also be viewed as [[finite state automata]]<ref name="KWM"/> and they have also found applications in [[semigroup|semigroup theory]] and in [[computer science]].<ref>Jean-Camille Birget, and Stuart W. Margolis. ''Two-letter group codes that preserve aperiodicity of inverse finite automata.'' Semigroup Forum, vol. 76 (2008), no. 1, pp. 159–168</ref><ref>D. S. Ananichev, A. Cherubini, M. V. Volkov. ''Image reducing words and subgroups of free groups.'' Theoretical Computer Science, vol. 307 (2003), no. 1, pp. 77–92.</ref><ref>J. Almeida, and M. V. Volkov. ''Subword complexity of profinite words and subgroups of free profinite semigroups.'' International Journal of Algebra and Computation, vol. 16 (2006), no. 2, pp. 221–258.</ref><ref>Benjamin Steinberg. ''A topological approach to inverse and regular semigroups.'' Pacific Journal of Mathematics, vol. 208 (2003), no. 2, pp. 367–396</ref>
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| Stallings' foldings method has been generalized and applied to other contexts, particularly in [[Bass-Serre theory]] for approximating group actions on [[tree (graph theory)|trees]] and studying the subgroup structure of the [[Bass-Serre theory|fundamental groups of graphs of groups]]. The first paper in this direction was written by Stallings himself,<ref>John R. Stallings. ''Foldings of G-trees.'' Arboreal group theory (Berkeley, CA, 1988), pp. 355–368, Math. Sci. Res. Inst. Publ., 19, Springer, New York, 1991; ISBN 0-387-97518-7</ref> with several subsequent generalizations of Stallings' folding methods in the [[Bass-Serre theory]] context by other mathematicians.<ref>Mladen Bestvina and Mark Feighn. ''Bounding the complexity of simplicial group actions on trees'', [[Inventiones Mathematicae]], vol. 103, (1991), no. 3, pp. 449–469</ref><ref>M. J. Dunwoody.
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| [http://msp.warwick.ac.uk/gtm/1998/01/p007.xhtml ''Folding sequences.''] The Epstein birthday schrift, pp. 139–158 (electronic),
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| Geometry and Topology Monographs, 1, Geom. Topol. Publ., Coventry, 1998.</ref><ref>Ilya Kapovich, Richard Weidmann, and Alexei Miasnikov. ''Foldings, graphs of groups and the membership problem.'' International Journal of Algebra and Computation, vol. 15 (2005), no. 1, pp. 95–128.</ref><ref>Yuri Gurevich, and Paul E. Schupp. ''Membership problem for the modular group.'' SIAM Journal on Computing, vol. 37 (2007), no. 2, pp. 425–459</ref>
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| Stallings' 1991 paper ''"Non-positively curved triangles of groups"''<ref>John R. Stallings. ''Non-positively curved triangles of groups.'' Group theory from a geometrical viewpoint (Trieste, 1990), pp. 491–503, World Sci. Publ., River Edge, NJ, 1991; ISBN 981-02-0442-6</ref> introduced and studied the notion of a [[Orbifold#Triangles of groups|triangle of groups]]. This notion was the starting point for the theory of [[Orbifold#Complexes of groups|complexes of groups]] (a higher-dimensional analog of [[Bass-Serre theory]]), developed by Haefliger<ref>[[André Haefliger]]. Complexes of groups and orbihedra. in: "Group theory from a geometrical viewpoint (Trieste, 1990)", pp. 504–540, World Sci. Publ., River Edge, NJ, 1991. ISBN 981-02-0442-6</ref> and others.<ref>Jon Corson. ''Complexes of groups.'' [[Proceedings of the London Mathematical Society]] (3) 65 (1992), no. 1, pp. 199–224.</ref><ref>Martin R. Bridson, and André Haefliger. Metric spaces of non-positive curvature. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319. Springer-Verlag, Berlin, 1999. ISBN 3-540-64324-9</ref> Stallings' work pointed out the importance of imposing some sort of "non-positive curvature" conditions on the complexes of groups in order for the theory to work well; such restrictions are not necessary in the one-dimensional case of [[Bass-Serre theory]].
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| Among Stallings' contributions to [[3-manifold|3-manifold topology]], the most well-known is the ''Stallings fibration theorem''.<ref>John R. Stallings. ''On fibering certain 3-manifolds.'' 1962 Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) pp. 95–100. Prentice-Hall, Englewood Cliffs, N.J</ref> The theorem states that if ''M'' is a compact irreducible [[3-manifold]] whose [[fundamental group]] contains a [[normal subgroup]], such that this subgroup is [[finitely generated group|finitely generated]] and such that the [[quotient group]] by this subgroup is [[infinite cyclic group|infinite cyclic]], then ''M'' [[Fibration|fibers]] over a circle. This is an important structural result in the theory of [[Haken manifold]]s that engendered many alternative proofs, generalizations and applications (e.g.<ref>John Hempel, and William Jaco. ''3-manifolds which fiber over a surface.'' [[American Journal of Mathematics]], vol. 94 (1972), pp. 189–205</ref><ref>Alois Scharf. ''Zur Faserung von Graphenmannigfaltigkeiten.'' (in German)
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| Mathematische Annalen, vol. 215 (1975), pp. 35–45.</ref><ref>Louis Zulli. ''Semibundle decompositions of 3-manifolds and the twisted cofundamental group.''
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| Topology and its Applications, vol. 79 (1997), no. 2, pp. 159–172</ref><ref>Nathan M. Dunfield, and Dylan P. Thurston. [http://www.msp.warwick.ac.uk/gt/2006/10/p055.xhtml ''A random tunnel number one 3-manifold does not fiber over the circle.''] [[Geometry & Topology]], vol. 10 (2006), pp. 2431–2499</ref> ), including a higher-dimensional analog.<ref>W. Browder, and J. Levine.
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| [http://www.springerlink.com/content/6832937w73322373/ ''Fibering manifolds over a circle.''] [[Commentarii Mathematici Helvetici]], vol. 40 (1966), pp. 153–160</ref>
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| A 1965 paper of Stallings ''"How not to prove the Poincaré conjecture"''<ref name="HNTPPC">John R. Stallings. [http://math.berkeley.edu/~stall/notPC.pdf ''How not to prove the Poincaré conjecture''.] Topology Seminar, Wisconsin, 1965.
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| Edited by R. H. Bing and R. J. Bean. Annals of Mathematics Studies, No. 60. [[Princeton University Press]], Princeton, N.J. 1966</ref> gave a [[group theory|group-theoretic]] reformulation of the famous [[Poincaré conjecture]]. The paper began with a humorous admission: "I have committed the sin of falsely proving Poincare's Conjecture. But that was in another country; and besides, until now, no one has known about it."<ref name="UCBPR"/><ref name="HNTPPC"/> Despite its ironic title, Stallings' paper informed much of the subsequent research on exploring the algebraic aspects of the [[Poincaré Conjecture]] (see, for example,<ref>Robert Myers. [http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=57081&fulltextType=RA&fileId=S0305004100004631 ''Splitting homomorphisms and the geometrization conjecture.''] Mathematical Proceedings of the Cambridge Philosophical Society, vol. 129 (2000), no. 2, pp. 291–300</ref><ref>Tullio Ceccherini-Silberstein. [http://www.springerlink.com/content/un4rk51at6r1cr3h/ ''On the Grigorchuk-Kurchanov conjecture.'']
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| Manuscripta Mathematica 107 (2002), no. 4, pp. 451–461</ref><ref>V. N. Berestovskii. ''Poincaré's conjecture and related statements.'' (in Russian) Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. vol. 51 (2000), no. 9, pp. 3–41; translation in Russian Mathematics (Izvestiya VUZ. Matematika), vol. 51 (2007), no. 9, 1–36</ref><ref>V. Poenaru. ''Autour de l'hypothèse de Poincaré''. in: "Géométrie au XXe siècle, 1930–2000 : histoire et horizons". Montréal, Presses internationales Polytechnique, 2005. ISBN 2-553-01399-X, 9782553013997.</ref>).
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| == Selected works ==
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| * {{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=Polyhedral homotopy spheres | mr=0124905 | year=1960 | journal=Bulletin of the American Mathematical Society | volume=66 | pages=485–488 | url=http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183523757}}
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| * {{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=The piecewise-linear structure of Euclidean space | mr=0149457 | year=1962 | journal=Proceedings of the Cambridge Philosophical Society | volume=58 | issue=03 | pages=481–488 | doi=10.1017/S0305004100036756 | last2=Zeeman | first2=E. C.}}
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| *{{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) | publisher=[[Prentice Hall]] | mr=0158375 | year=1962 | chapter=On fibering certain 3-manifolds | pages=95–100}}
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| * {{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=Homology and central series of groups | doi=10.1016/0021-8693(65)90017-7 | mr=0175956 | year=1965 | journal=Journal of Algebra | volume=2 | issue=2 | pages=170–181 | url=http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-4D7K7V7-1ND&_user=10&_coverDate=06%2F30%2F1965&_rdoc=2&_fmt=high&_orig=browse&_srch=doc-info(%23toc%236838%231965%23999979997%23518386%23FLP%23display%23Volume)&_cdi=6838&_sort=d&_docanchor=&_ct=4&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=8ab7d96d2a5bc830377ddb428f668224}}
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| * {{Citation | last1=Stallings | first1=John | author1-link=John R. Stallings | title=A finitely presented group whose 3-dimensional integral homology is not finitely generated | mr=0158917 | year=1963| journal=[[American Journal of Mathematics]] | volume=85 | pages=541–543 | doi=10.2307/2373106 | jstor=2373106 | issue=4 | publisher=The Johns Hopkins University Press}}
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| * {{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=On torsion-free groups with infinitely many ends | doi=10.2307/1970577 | mr=0228573 | year=1968 | journal=[[Annals of Mathematics|Annals of Mathematics. Second Series]] | volume=88 | pages=312–334 | issue=2 | publisher=Annals of Mathematics | jstor=1970577}}
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| *{{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=Group theory and three-dimensional manifolds | publisher=[[Yale University Press]] | mr=0415622 | year=1971|isbn=0-300-01397-3}}
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| *{{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2 | publisher=[[American Mathematical Society]] | location=Providence, R.I. | series=Proc. Sympos. Pure Math., XXXII | mr=520522 | year=1978 | chapter=Constructions of fibred knots and links | pages=55–60}}
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| * {{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=Topology of finite graphs | doi=10.1007/BF02095993 | mr=695906 | year=1983 | journal=[[Inventiones Mathematicae]] | volume=71 | issue=3 | pages=551–565 | url=http://www.springerlink.com/content/mn2h645qw2058530/}}, with over 100 recent citations
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| *{{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=Arboreal group theory (Berkeley, CA, 1988)| publisher=Springer | location=New York | series=Mathematical Sciences Research Institute Publications|volume =19 | mr=1105341 | year=1991 | chapter=Folding ''G''-trees| pages=355–368| isbn=0-387-97518-7}}
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| *{{Citation | last1=Stallings | first1=John R. | author1-link=John R. Stallings | title=Group theory from a geometrical viewpoint (Trieste, 1990) | publisher=World Scientific | location=River Edge, NJ| mr=1170374 | year=1991 | chapter=Non-positively curved triangles of groups | pages=491–903|isbn=981-02-0442-6}}
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| ==Notes==
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| {{reflist}}
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| == External links ==
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| * {{MathGenealogy|id=452}}
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| *[http://math.berkeley.edu/~stall/ home page] of John Stallings.
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| *[http://www.ams.org/notices/200911/rtx091101410p.pdf Remembering John Stallings,] [[Notices of the American Mathematical Society]], vol. 56 (2009), no. 11, pp. 1410 1417
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| {{Authority control|VIAF=93821690}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Stallings, John R. Jr.
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = American mathematician
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| | DATE OF BIRTH = July 22, 1935
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| | PLACE OF BIRTH = [[Morrilton, Arkansas]], [[United States]]
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| | DATE OF DEATH = November 24, 2008
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| | PLACE OF DEATH = [[Berkeley, California]], [[United States]]
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| }}
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| {{DEFAULTSORT:Stallings, John R. Jr.}}
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| [[Category:1935 births]]
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| [[Category:2008 deaths]]
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| [[Category:American mathematicians]]
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| [[Category:Group theorists]]
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| [[Category:Topologists]]
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| [[Category:20th-century mathematicians]]
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| [[Category:21st-century mathematicians]]
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| [[Category:University of Arkansas alumni]]
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| [[Category:Princeton University alumni]]
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| [[Category:University of California, Berkeley faculty]]
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