Hyperbolic groupoids and duality Academic Article uri icon


  • 2015 American Mathematical Society. We introduce 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. We describe a duality theory for hyperbolic groupoids. We show that for every hyperbolic groupoid G there is a naturally defined dual groupoid GT acting on the Gromov boundary of a Cayley graph of G. The groupoid GT is also hyperbolic and such that (GT)T is equivalent to G. Several classes of examples of hyperbolic groupoids and their applications are discussed.

published proceedings

  • Memoirs of the American Mathematical Society

author list (cited authors)

  • Nekrashevych, V.

citation count

  • 5

complete list of authors

  • Nekrashevych, Volodymyr

publication date

  • September 2015