Topology Seminar: Ian Putnam (University of Victoria)

As part of Smale's program for smooth dynamics, David Ruelle gave a definition of a Smale space as (roughly) a topological dynamical system which has a local product structure of contracting and expanding directions for the dynamics. A special case is certain symbolic dynamical systems called shifts of finite type. In the late 1970's, Wolfgang Krieger, motivated by ideas from C*-algebra theory and K-theory, provided a beautiful algebraic invariant for shifts of finite type. The aim of this talk is to show how this invariant may be extended to the class of all Smale spaces as a kind of homology theory which provides a Lefschetz formula. Such a theory was conjectured by Bowen. (I will attempt to define and give examples of all the dynamical concepts: Smale space, shifts of finite type, etc.)