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Hyperbolic Groupoids and Duality
 
Volodymyr Nekrashevych Texas A & M University, College Station, Texas
Hyperbolic Groupoids and Duality
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
Hyperbolic Groupoids and Duality
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Hyperbolic Groupoids and Duality
Volodymyr Nekrashevych Texas A & M University, College Station, Texas
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 Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2372015; 108 pp
    MSC: 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2372015; 108 pp
MSC: 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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