Euler homology

Details Euler homology Euler homology

2006-06-22

arxiv.org/abs/math/0606558v1

Mathematics

Algebraic Topology

20 pages, to be published in Mathematische Zeitschrift

Scientific paper

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.

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