Homology and K-theory of dynamical systems. I. torsion-free ample groupoids
K-Theory and Homology
2022-07-12 v4 Dynamical Systems
Operator Algebras
Abstract
Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the K-groups of the (reduced) groupoid C*-algebra, provided the groupoid has torsion-free stabilizers and satisfies a strong form of the Baum-Connes conjecture. The construction is based on the triangulated category approach to the Baum-Connes conjecture developed by Meyer and Nest. We also present a few applications to topological dynamics and discuss the HK conjecture of Matui.
Keywords
Cite
@article{arxiv.2006.08028,
title = {Homology and K-theory of dynamical systems. I. torsion-free ample groupoids},
author = {Valerio Proietti and Makoto Yamashita},
journal= {arXiv preprint arXiv:2006.08028},
year = {2022}
}
Comments
v4: 23 pages, post-publication notes; v3: 23 pages, new title, Smale space part is split off as arXiv:2104.10938, to appear in Ergodic Theory Dynam. Systems; v2: 38 pages, some remarks and appendix expanded; v1: 34 pages