Event Details

Speaker: Andrew Toms (Purdue University, Indiana)

Title: Homotopy groups of Cuntz classes in C*-algebras

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.