Hyperbolic Groupoids and Duality

Released on by Volodymyr Nekrashevych
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  • Hyperbolic Groupoids and Duality Book Detail

  • Author : Volodymyr Nekrashevych
  • Release Date : 2015-08-21
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 120
  • ISBN 13 : 1470415445
  • File Size : 22,22 MB
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Hyperbolic Groupoids and Duality by Volodymyr Nekrashevych PDF Summary

Book Description: 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 G there is a naturally defined dual groupoid G⊤ acting on the Gromov boundary of a Cayley graph of G. The groupoid G⊤ is also hyperbolic and such that (G⊤)⊤ is equivalent to G. Several classes of examples of hyperbolic groupoids and their applications are discussed.

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