
eBook ISBN: | 978-1-4704-2511-1 |
Product Code: | MEMO/237/1122.E |
List Price: | $80.00 |
MAA Member Price: | $72.00 |
AMS Member Price: | $48.00 |

eBook ISBN: | 978-1-4704-2511-1 |
Product Code: | MEMO/237/1122.E |
List Price: | $80.00 |
MAA Member Price: | $72.00 |
AMS Member Price: | $48.00 |
-
Book DetailsMemoirs of the American Mathematical SocietyVolume: 237; 2015; 108 ppMSC: Primary 37; 20
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
-
Chapters
-
Introduction
-
1. Technical preliminaries
-
2. Preliminaries on groupoids and pseudogroups
-
3. Hyperbolic groupoids
-
4. Smale quasi-flows and duality
-
5. Examples of hyperbolic groupoids and their duals
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
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.
-
Chapters
-
Introduction
-
1. Technical preliminaries
-
2. Preliminaries on groupoids and pseudogroups
-
3. Hyperbolic groupoids
-
4. Smale quasi-flows and duality
-
5. Examples of hyperbolic groupoids and their duals