Equivariant Lefschetz maps for simplicial complexes and smooth manifolds

Date

2009-11

Authors

Emerson, Heath
Meyer, Ralf

Journal Title

Journal ISSN

Volume Title

Publisher

Mathematische Annalen

Abstract

Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of Lefschetz numbers for self-maps to an equivariant K-homology class. We compute the Lefschetz invariants for self-maps of finite-dimensional simplicial complexes and smooth manifolds. The resulting invariants are independent of the extra structure used to compute them. Since smooth manifolds can be triangulated, we get two formulas for the same Lefschetz invariant in this case. The resulting identity is closely related to the equivariant Lefschetz Fixed Point Theorem of Lück and Rosenberg.

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Citation

Emerson, H., and Meyer, R. (2009). Equivariant Lefschetz maps for simplicial complexes and smooth manifolds. Mathematische Annalen, 345(3), 599-630. https://doi.org/10.1007/s00208-009-0367-z