On rigidity of Roe algebras, Rufus Willet, Vanderbilt University, Wed, 20 April, 2011, 10:00 a.m. C-236

Abstract

The Roe algebra associated to a metric space X is a noncommutative C*-algebra originally defined by Roe in the course of his work on index theory on non-compact manifolds. It has since seen many applications in geometry and topology, perhaps most notably through the coarse Baum-Connes conjecture: this predicts that the Roe algebra is a good model for the large-scale geometry of the original metric space, at least on the level of algebraic topology. It is thus natural to ask how much of the geometry of a space can be recovered from its Roe algebra: in particular, if metric spaces X and Y have isomorphic Roe algebras, must they have the same large scale geometry? I will present joint work with Jan Spakula on this question, which we show quite often has a positive answer.