A homology theory for Smale spaces
Author(s)
Bibliographic Information
A homology theory for Smale spaces
（Memoirs of the American Mathematical Society, no. 1094）
American Mathematical Society, c2014
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Note
"Volume 232, number 1094 (sixth of 6 numbers), November 2014"
Includes bibliographical references (p. 121-122)
Description and Table of Contents
Description
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.
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