Hyperbolic groupoids and duality
著者
書誌事項
Hyperbolic groupoids and duality
（Memoirs of the American Mathematical Society, v. 237,
American Mathematical Society, 2015
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注記
Includes bibliographical references (p. 103-105) and index
内容説明・目次
内容説明
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.
目次
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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