A Homology Theory for Smale Spaces

Download or read book A Homology Theory for Smale Spaces written by Ian F. Putnam and published by American Mathematical Soc.. This book was released on 2014-09-29 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.