Nuclear dimension of $C^*$-algebras of homeomorphisms

Ilan Hirshberg  (Ben Gurion University of the Negev)

10:00 am - 11:00 am, May 13th, 2016   Science Building A1510

Abstract:

Suppose $X$ is a compact metrizable space with finite covering dimension, and $h$ a homeomorphism of $X$. Let $A$ be the crossed product of $C(X)$ by the induced automorphism. It was shown first by Toms and Winter, and in a different way by the speaker, Winter and Zacharias, that if $h$ is a minimal homeomorphism then $A$ has finite nuclear dimension. Szabo then showed that it suffices to assume that $h$ is free.
In this talk, I'll discuss a recent result which settles the issue for arbitrary homeomorphisms. As a special case, we show that group $C^*$-algebras of certain non-nilpotent groups have finite nuclear dimension. Time permitting, I will discuss some work in progress concerning the analogous result for flows.
This is joint work with Jianchao Wu.