Ralf Meyer lectures     19-21 January 2011

 

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Ralf Meyer (Göttingen) will be delivering a series of lectures on:

 

Geometric models for equivariant bivariant K-theory

 

Abstract:


We use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. Our construction uses no special features of equivariant K-theory. To highlight this, we construct bivariant extensions for arbitrary equivariant multiplicative cohomology theories.

We formulate necessary and sufficient conditions for certain duality isomorphisms in the topological bivariant K-theory and verify these conditions in some cases, including smooth manifolds with a smooth cocompact action of a Lie group. One of these duality isomorphisms reduces bivariant K-theory to K-theory with support conditions. Since similar duality isomorphisms exist in Kasparov theory, the topological and analytic bivariant K-theories agree if there is such a duality isomorphism.

This is joint work with Heath Emerson, which appeared in Adv. Math. 225 (2010), 2840-2882 and 2883-2919.

 

 

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