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
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.
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