A Homology Theory for Smale Spaces

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  • A Homology Theory for Smale Spaces Book Detail

  • Author : Ian F. Putnam
  • Release Date : 2014-09-29
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 136
  • ISBN 13 : 1470409097
  • File Size : 39,39 MB

A Homology Theory for Smale Spaces by Ian F. Putnam PDF Summary

Book 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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