Homotopy groups of Cuntz classes in C*-algebras

Andrew Toms (Purdue University)

Thursday 16th October 16:00-17:00
Maths116

Abstract

The Cuntz semigroup of a C*-algebra A consists of equivalence classes of positive elements, where equivalence means roughly that two positive elements have the same rank relative to A.  It can be thought of as a generalization of the Murray von Neumann semigroup to positive elements and is an incredibly sensitive invariant.  We give a brief introduction to this object and its relevance to the classification theory of separable nuclear C*-algebras.  We then present a calculation of the homotopy groups of these Cuntz classes as topological subspaces of A when A is classifiable in the sense of Elliott.

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