K-theory and homology of Smale spaces

Valerio Proietti (East China Normal University)

Thursday 27th February, 2020 15:00-16:00 Maths 311B


Smale spaces have been introduced by Ruelle as an abstraction of the basic sets of an Axiom A system. They are topological dynamical systems of hyperbolic nature. Later Putnam has defined a homology theory for such systems, based on the notion of dimension group for shifts of finite type, and relying an an improved version of a Theorem of Bowen in symbolic dynamics. In this lecture we will focus on Smale spaces whose stable sets are totally disconnected. This class is fairly large and includes tiling spaces, solenoids, quasicrystals, etc. I will discuss the connections between Putnam's homology, groupoid homology (à la Matui), and K-theory for C*-algebras which are naturally associated to Smale spaces.

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