Memoirs of the American Mathematical Society 2014; 122 pp; softcover Volume: 232 ISBN10: 1470409097 ISBN13: 9781470409098 List Price: US$76 Individual Members: US$45.60 Institutional Members: US$60.80 Order Code: MEMO/232/1094
 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 finitetoone 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. Table of Contents  Summary
 Dynamics
 Dimension groups
 The complexes of an \(s/u\)bijective factor map
 The double complexes of an \(s/u\)bijective pair
 A Lefschetz formula
 Examples
 Questions
 Bibliography
