Dualities in equivariant Kasparov theory

Details Dualities in equivariant Kasparov theory Dualities in equivariant Kasparov theory

2007-10-31

arxiv.org/abs/0711.0025v3

New York J. Math. 16 (2010), 245-313, http://www.emis.de/journals/NYJM/nyjm/NYJM/j/2010/16-12.html

Mathematics

K-Theory and Homology

Significant changes, mainly variants of the duality isomorphisms with different support conditions and applications

Scientific paper

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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