Acyclic space: Difference between revisions
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* [[Contractible space]] | * [[Contractible space]] | ||
* [[Weakly contractible space]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
Revision as of 23:58, 1 December 2007
This article defines a property of topological spaces that depends only on the homology of the topological space, viz it is completely determined by the homology groups. In particular, it is a homotopy-invariant property of topological spaces
View all homology-dependent properties of topological spaces OR view all homotopy-invariant properties of topological spaces OR view all properties of topological spaces
This is a variation of contractibility. View other variations of contractibility
Definition
A topological space is said to be acyclic if the homology groups in all dimensions are the same as those of a point, for any homology theory. Equivalently, it suffices to say that the singular homology groups are the same as those for a point.
Relation with other properties
Stronger properties
Weaker properties
Metaproperties
A product of acyclic spaces is acyclic. The proof of this relies on the Kunneth formula.