Hyperbolic Groupoids and Duality
Seiten
2015
American Mathematical Society (Verlag)
978-1-4704-1544-0 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-1544-0 (ISBN)
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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.
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.
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.
Volodymyr Nekrashevych, Texas A & M University, College Station, Texas, USA.
Introduction
Technical preliminaries
Preliminaries on groupoids and pseudogroups
Hyperbolic groupoids
Smale quasi-flows and duality
Examples of hyperbolic groupoids and their duals
Bibliography
Index
| Erscheint lt. Verlag | 1.9.2015 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 183 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-1544-5 / 1470415445 |
| ISBN-13 | 978-1-4704-1544-0 / 9781470415440 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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