Putnam defines a type of homology theory for Smale spaces, which include the basic sets for Smale's Axiom A diffeomorphism.. His approach is founded on two pillars. One 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 other is Krieger's dimension group invariant for shifts of finite type. He covers dynamics, dimensional groups, the complexes of an s/u-bijective factor map, the double complexes of an s/u-bijective pair, a Lefschetz formula, examples, and questions. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)