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Connective C*-algebras (Ulrich Pennig, Cardiff University)

When 09 Nov 2018
from 02:00 PM to 04:00 PM
Where B.02.18
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Abstract: Topological K-theory and K-homology can be generalised to bivariant E-theory of C*-algebras. The group E(A,B) is defined in terms of asymptotic morphisms between stabilised suspensions of both algebras. Since unsuspended asymptotic morphisms contain a priori more geometric information, the question arises, in what situations we can avoid suspension.

This talk is about a joint project with M. Dadarlat, in which we study a homotopy invariant property called connectivity, which gives a complete answer in the case of nuclear algebras. It has a lot of other interesting implications like absence of nonzero projections and quasidiagonality, and it has good permanence properties. Connectivity is closely related to the topology of the primitive ideal space of an algebra.

In the talk I will give a short introduction to asymptotic morphisms and then discuss some of our results about connectivity of augmentation ideals and Lie group C*-algebras.