Functional Analysis Seminar | Mathematical Institute

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series

Tue, 14 Oct 2025
16:00

Homotopy groups of Cuntz classes in C*-algebras

Andrew Toms

(Leverhulme Visiting Professor, University of Oxford)

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 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. Remarkably, outside the case of compact classes, these spaces turn out to be contractible.