October 23rd 2017; 15:00; Seminar room C3b/158
Kang Li, Rigidity and K-theory of uniform Roe algebras over non-amenable metric spaces
Abstract: I will report on recent developments related to rigidity and K-theory of uniform Roe algebras associated to non-amenable metric spaces with bounded geometry. I will explain the following results:
1. If the metric space X is non-amenable and has asymptotic dimension one, then the K0 group of the uniform Roe algebra over X is always zero. We also answer negatively to a question of Elliott and Sierakowski about the vanishing of K0 of the uniform Roe algebras of non-amenable groups.
2. If X and Y are non-amenable property A metric spaces, then their uniform Roe algebras are *-isomorphic if and only if there is a bijective coarse equivalence between X and Y.