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arXiv · 0711.0025

Dualities in equivariant Kasparov theory

Heath Emerson·Ralf Meyer
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Abstract

We study several duality isomorphisms between equivariant bivariant K-theory groups, generalising Kasparov's first and second Poincare duality isomorphisms. We use the first duality to define an equivariant generalisation of Lefschetz invariants of generalised self-maps. The second duality is related to the description of bivariant Kasparov theory for commutative C*-algebras by families of elliptic pseudodifferential operators. For many groupoids, both dualities apply to a universal proper G-space. This is a basic requirement for the dual Dirac method and allows us to describe the Baum-Connes assembly map via localisation of categories.

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Heath Emerson, Ralf Meyer. 2009-07-24. Dualities in equivariant Kasparov theory. https://arxiv.org/abs/0711.0025

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