A Homology Theory for Smale Spaces, Paperback / softback Book

A Homology Theory for Smale Spaces Paperback / softback

Part of the Memoirs of the American Mathematical Society series

Paperback / softback

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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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