Dualities in equivariant Kasparov theory
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.
Cite
@article{arxiv.0711.0025,
title = {Dualities in equivariant Kasparov theory},
author = {Heath Emerson and Ralf Meyer},
journal= {arXiv preprint arXiv:0711.0025},
year = {2011}
}
Comments
Significant changes, mainly variants of the duality isomorphisms with different support conditions and applications