Euler homology |
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Authors: | Julia Weber |
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Institution: | (1) Max–Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany |
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Abstract: | We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented
cobordism ring of a topological space X. This homology theory Eh
* has coefficients in every nonnegative dimension. There exists a natural transformation that for X = pt assigns 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 of graded -modules is shown for any CW-complex X. For discrete groups G, we also define an equivariant version of the homology theory Eh
*, generalizing the equivariant Euler characteristic. |
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Keywords: | Primary 55N20 Primary 57R90 Primary 57R99 Secondary 55N91 Secondary 57R85 |
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