Van Hove singularity: Difference between revisions

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In [[homological algebra]], a branch of [[mathematics]], a '''quasi-isomorphism''' is a morphism ''A'' → ''B'' of [[chain complex]]es (respectively, cochain complexes) such that the induced morphisms 
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:<math>H_n(A_\bullet) \to H_n(B_\bullet)\ (\text{respectively, } H^n(A^\bullet) \to H^n(B^\bullet))\ </math>
 
of [[homology (mathematics)|homology]] groups (respectively, of cohomology groups) are isomorphisms for all ''n''.
 
In the theory of [[model category|model categories]], quasi-isomorphisms are sometimes used as the class of [[weak equivalence (homotopy theory)|weak equivalence]]s when the objects of the category are chain or cochain complexes. This results in a homology-local theory, in the sense of [[Bousfield localization]] in [[homotopy theory]].
 
==References==
*Gelfand, Manin. ''Methods of Homological Algebra'', 2nd ed. Springer, 2000.
 
[[Category:Algebraic topology]]
[[Category:Homological algebra]]

Revision as of 06:28, 22 February 2014

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