Connective C*-algebras

Ulrich Pennig (Cardiff University)

Tuesday 10th October, 2017 16:00-17:00 311B


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, when we can avoid suspension. In joint work with Marius Dadarlat, we studied a homotopy invariant property called connectivity, which gives a complete answer in the nuclear case. It has a lot of other interesting implications like absence of nonzero projections and quasidiagonality and it has good permanence properties. In the talk I will explain connectivity and will then discuss examples and counterexamples for connective C*-algebras.

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