**Memoirs of the American Mathematical Society**

2015;
108 pp;
Softcover

MSC: Primary 37; 20;

Print ISBN: 978-1-4704-1544-0

Product Code: MEMO/237/1122

List Price: $80.00

Individual Member Price: $48.00

**Electronic ISBN: 978-1-4704-2511-1
Product Code: MEMO/237/1122.E**

List Price: $80.00

Individual Member Price: $48.00

# Hyperbolic Groupoids and Duality

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*Volodymyr Nekrashevych*

The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding self-coverings, natural pseudogroups acting on leaves of stable (or unstable) foliation of an Anosov diffeomorphism, etc.

The author describes a duality theory for hyperbolic groupoids. He shows that for every hyperbolic groupoid \(\mathfrak{G}\) there is a naturally defined dual groupoid \(\mathfrak{G}^\top\) acting on the Gromov boundary of a Cayley graph of \(\mathfrak{G}\). The groupoid \(\mathfrak{G}^\top\) is also hyperbolic and such that \((\mathfrak{G}^\top)^\top\) is equivalent to \(\mathfrak{G}\).

Several classes of examples of hyperbolic groupoids and their applications are discussed.

#### Table of Contents

# Table of Contents

## Hyperbolic Groupoids and Duality

- Cover Cover11 free
- Title page i2 free
- Introduction 18 free
- Chapter 1. Technical preliminaries 916
- Chapter 2. Preliminaries on groupoids and pseudogroups 3138
- Chapter 3. Hyperbolic groupoids 4956
- Chapter 4. Smale quasi-flows and duality 6774
- Chapter 5. Examples of hyperbolic groupoids and their duals 8996
- Bibliography 103110
- Index 107114 free
- Back Cover Back Cover1120