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- Title
Euler homology.
- Authors
Julia Weber
- Abstract
Abstract??We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring$${\mathcal{n}_*(x)}$$of a topological spaceX. This homology theoryEh*has coefficients$${\mathbb{z}/2}$$in every nonnegative dimension. There exists a natural transformation$${\mathcal{n}_*(x)\to eh_*(x)}$$that forX?=?ptassigns to each smooth manifold its Euler characteristic mod 2. The homology theory is constructed using cobordism of stratifolds, which are singular objects defined below. An isomorphism$${eh_*(x)\cong h_*(x;\mathbb{z}/2)\otimes_{\mathbb{z}/2} \mathbb{z}/2[t]}$$of graded$${\mathcal{n}_*}$$-modules is shown for any CW-complexX. For discrete groupsG, we also define an equivariant version of the homology theoryEh*, generalizing the equivariant Euler characteristic.
- Subjects
HOMOLOGY theory; SET theory; TECHNICAL specifications; ALGEBRAIC topology
- Publication
Mathematische Zeitschrift, 2007, Vol 256, Issue 1, p57
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-006-0059-2