Hyperbolic Groupoids and Duality
Author: Volodymyr Nekrashevych
Publisher: American Mathematical Soc.
Published: 2015-08-21
Total Pages: 120
ISBN-13: 1470415445
DOWNLOAD EBOOKThe 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.