Euler homology
Algebraic Topology
2007-05-23 v1
Abstract
We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative dimension. There exists a natural transformation N_*(X)->Eh_*(X) that for X=pt assigns to each smooth manifold its Euler characteristic mod 2. The homology theory is constructed using cobordism of stratifolds. For discrete groups G, we also define an equivariant version of the homology theory Eh_*, generalizing the equivariant Euler characteristic.
Cite
@article{arxiv.math/0606558,
title = {Euler homology},
author = {Julia Weber},
journal= {arXiv preprint arXiv:math/0606558},
year = {2007}
}
Comments
20 pages, to be published in Mathematische Zeitschrift