Title: Homology and K-theory of dynamical systems
Abstract: Smale spaces give an interesting class of hyperbolic dynamics closely connected to symbolic dynamics. We relate the following homological invariants associated with Smale spaces: Crainic and Moerdijk's homology of étale groupoid for the unstable equivalence relation, Putnam's homology based on resolution by symbolic dynamics, and K-groups of the étale groupoid. As an application, we obtain the finiteness of rank of the K-groups as conjectured by Kaminker, Putnam, and Whittaker. Based on joint works by Valerio Proietti.