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86,94 €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 ?? there is a naturally defined dual groupoid ??? acting on the Gromov boundary of a Cayley graph of ??. The groupoid ??? is also hyperbolic and such that (???)? is equivalent to ??.
Several classes of examples of hyperbolic groupoids and their applications are discussed.
Author
Volodymyr Nekrashevych, Texas A & M University, College Station, Texas
Table of Contents
Introduction
Technical preliminaries
Preliminaries on groupoids and pseudogroups
Hyperbolic groupoids
Smale quasi-flows and duality
Examples of hyperbolic groupoids and their duals
Bibliography
Index
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