**Memoirs of the American Mathematical Society**

2014;
122 pp;
Softcover

MSC: Primary 37;

Print ISBN: 978-1-4704-0909-8

Product Code: MEMO/232/1094

List Price: $76.00

AMS Member Price: $45.60

MAA Member Price: $68.40

**Electronic ISBN: 978-1-4704-1897-7
Product Code: MEMO/232/1094.E**

List Price: $76.00

AMS Member Price: $45.60

MAA Member Price: $68.40

# A Homology Theory for Smale Spaces

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*Ian F. Putnam*

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

# Table of Contents

## A Homology Theory for Smale Spaces

- Cover Cover11 free
- Title page i2 free
- Preface vii8 free
- Chapter 1. Summary 110 free
- Chapter 2. Dynamics 1120
- Chapter 3. Dimension groups 3746
- Chapter 4. The complexes of an 𝑠/𝑢-bijective factor map 5564
- Chapter 5. The double complexes of an 𝑠/𝑢-bijective pair 8594
- Chapter 6. A Lefschetz formula 105114
- Chapter 7. Examples 113122
- Chapter 8. Questions 117126
- Bibliography 121130
- Back Cover Back Cover1136