Space with finitely generated homology: Difference between revisions
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==Definition== | ==Definition== | ||
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* [[Finite CW-space]] | * [[Finite CW-space]] | ||
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* [[Space with homology of finite type]] | * [[Space with homology of finite type]] | ||
* [[Space with finitely generated homology groups]] | |||
Latest revision as of 19:58, 11 May 2008
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
Definition
A topological space is said to have finitely generated homology if it has only finitely many nonzero homology groups, and each of them is a finitely generated group. In other words, the Betti numbers are all finite and only finitely many of them are nonzero.