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A Homology Theory for Smale Spaces
 
Ian F. Putnam :  University of Victoria, Victoria, British Columbia, Canada
A Homology Theory for Smale Spaces
eBook ISBN:  978-1-4704-1897-7
Product Code:  MEMO/232/1094.E
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $45.60
Add to cart
A Homology Theory for Smale Spaces
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A Homology Theory for Smale Spaces
Ian F. Putnam :  University of Victoria, Victoria, British Columbia, Canada
eBook ISBN:  978-1-4704-1897-7
Product Code:  MEMO/232/1094.E
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $45.60
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 232; 2014; 122 pp
    MSC: Primary 37

    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.
  • Table of Contents
     
     
    • Chapters
    • Preface
    • 1. Summary
    • 2. Dynamics
    • 3. Dimension groups
    • 4. The complexes of an $s/u$-bijective factor map
    • 5. The double complexes of an $s/u$-bijective pair
    • 6. A Lefschetz formula
    • 7. Examples
    • 8. Questions
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 232; 2014; 122 pp
MSC: Primary 37

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.
  • Chapters
  • Preface
  • 1. Summary
  • 2. Dynamics
  • 3. Dimension groups
  • 4. The complexes of an $s/u$-bijective factor map
  • 5. The double complexes of an $s/u$-bijective pair
  • 6. A Lefschetz formula
  • 7. Examples
  • 8. Questions
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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