en>EmausBot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:Q11990376

2013-04-26T07:53:18Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:Q11990376

← Older revision		Revision as of 09:53, 26 April 2013
Line 1:		Line 1:
	~~I am Oscar and I completely dig that name. Hiring~~ is ~~my occupation~~. ~~Playing baseball~~ is the ~~pastime he will by no means stop performing. For years he~~'~~s been residing in North Dakota~~ and ~~his family loves it.~~<br><br>~~Here~~ is ~~my web blog ::~~ [~~http~~://~~flashtrue~~.~~com~~/~~stay~~-~~yeast~~-~~infection~~-~~free~~-~~using~~-~~these~~-~~useful~~-~~tips~~/ ~~flashtrue~~.~~com~~]		'''Ganea's conjecture''' is a claim in [[algebraic topology]], now disproved. It states that
			: <math> \text{cat}(X \times S^n)=\text{cat}(X) +1, n>0 \,\!</math>
			where cat(''X'') is the [[Lusternik–Schnirelmann category]] of a [[topological space]] ''X'', and ''S''<sup>''n''</sup> is the ''n'' dimensional [[sphere]].

			The inequality
			: <math> \text{cat}(X \times Y) \le \text{cat}(X) +\text{cat}(Y) </math>
			holds for any pair of spaces, ''X'' and ''Y''. Furthermore, cat(''S''<sup>''n''</sup>)=1, for any sphere ''S''<sup>''n''</sup>, ''n''>0. Thus, the conjecture amounts to cat(''X'' × S<sup>''n''</sup>) ≥ cat(''X'') + 1.

			The conjecture was formulated by [[Tudor Ganea]] in 1971. Many particular cases of this conjecture were proved, till finally Norio Iwase gave a counterexample in 1998. In a follow-up paper from 2002, Iwase gave an even stronger counterexample, with ''X'' a closed, [[smooth manifold]]. This counterexample also disproved a related conjecture, stating that
			: <math> \text{cat}(M - {p})=\text{cat}(M) -1 , </math>
			for a closed manifold ''M'' and ''p'' a point in ''M''.

			This work raises the question: For which spaces ''X'' is the Ganea condition, cat(''X'' × S<sup>''n''</sup>) = cat(''X'') + 1, satisfied? It has been conjectured that these are precisely the spaces ''X'' for which cat(''X'') equals a related invariant, Qcat(''X'').

			==References==
			*{{cite journal \|first=Tudor \|last=Ganea \|title=Some problems on numerical homotopy invariants \|journal=Lecture Notes in Mathematics \|volume=249 \|publisher=[[Springer-Verlag]] \|location=Berlin \|year=1971 \|pages=13–22 \|mr=0339147 \|doi=10.1007/BFb0060892 }}
			*{{cite journal \|doi=10.1016/0040-9383(91)90006-P \|first=Kathryn \|last=Hess \|title=A proof of Ganea's conjecture for rational spaces \|journal=[[Topology (journal)\|Topology]] \|volume=30 \|year=1991 \|issue=2 \|pages=205–214 \|mr=1098914 }}
			*{{cite journal \|first=Norio \|last=Iwase \|title=Ganea's conjecture on Lusternik–Schnirelmann category \|journal=[[Bulletin of the London Mathematical Society]] \|volume=30 \|year=1998 \|issue=6 \|pages=623–634 \|doi=10.1112/S0024609398004548 \|mr=1642747 }}
			*{{cite journal \|doi=10.1016/S0040-9383(00)00045-8 \|first=Norio \|last=Iwase \|title=A<sub>∞</sub>-method in Lusternik–Schnirelmann category \|journal=Topology \|volume=41 \|year=2002 \|issue=4 \|pages=695–723 \|mr=1905835 }}
			*{{cite journal \|doi=10.1016/S0040-9383(02)00007-1 \|first=Lucile \|last=Vandembroucq \|title=Fibrewise suspension and Lusternik–Schnirelmann category \|journal=Topology \|volume=41 \|year=2002 \|issue=6 \|pages=1239–1258 \|mr=1923222 }}

			[[Category:Disproved conjectures]]
			[[Category:Algebraic topology]]

en>Michael Hardy: moved High Frequency Content measure to High frequency content measure

2011-08-15T01:11:02Z

moved High Frequency Content measure to High frequency content measure

New page

I am Oscar and I completely dig that name. Hiring is my occupation. Playing baseball is the pastime he will by no means stop performing. For years he's been residing in North Dakota and his family loves it.<br><br>Here is my web blog :: [http://flashtrue.com/stay-yeast-infection-free-using-these-useful-tips/ flashtrue.com]

High frequency content measure - Revision history

en>EmausBot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:Q11990376

en>Michael Hardy: moved High Frequency Content measure to High frequency content measure