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Equivariant Euler characteristics andK–homology Euler classes for proper cocompactG–manifolds

2003
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Geometry and Topology
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Let G be a countable discrete group and let M be a smooth proper cocompact G-manifold without boundary. The Euler operator defines via Kasparov theory an element, called the equivariant Euler class, in the equivariant K-homology of M. The universal equivariant Euler characteristic of M, which lives in a group U^G(M), counts the equivariant cells of M, taking the component structure of the various fixed point sets into account. We construct a natural homomorphism from U^G(M) to the equivariant

doi:10.2140/gt.2003.7.569
fatcat:uyletzkgxjbcxcqzms6nmo6uku