Space with Euler characteristic zero: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Compact connected Lie group]] (nontrivial) | * [[Compact connected Lie group]] (nontrivial): {{proofat|[[compact connected nontrivial Lie group implies zero Euler characteristic]]}} | ||
===Weaker properties=== | ===Weaker properties=== | ||
Revision as of 23:20, 1 February 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 zero Euler characteristic if it has finitely generated homology, and its Euler characteristic is zero.
Relation with other properties
Stronger properties
- Compact connected Lie group (nontrivial): For full proof, refer: compact connected nontrivial Lie group implies zero Euler characteristic