Speaker: Makoto Yamashita (Univ. Oslo)

Title: Homology and K-theory of torsion free ample groupoids and Smale spaces

Time/Date: 4:45-6:15pm, June 11 (Thu.), 2020

Room: This will be an online seminar on Zoom. Please ask Kawahigashi for the Zoom link.

Abstract: Given an ample groupoid, we construct a spectral sequence which consists of the groupoid homology in integral coefficient on the second sheet, converging to the K-groups of the groupoid C^*-algebra when the groupoid has torsion free stabilizers and satisfies the strong Baum-Connes conjecture. The construction is based on the triangulated categorical approach to the Baum-Connes conjecture by Meyer and Nest. For the unstable equivalence relation of a Smale space with totally disconnected stable sets, this spectral sequence shows Putnam's homology groups on the second sheet. This is a joint work with Valerio Proietti.