How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2213  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046
Email: cust-serv@ams.org

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax
  Remote Access

Hyperbolic groupoids and duality


About this Title

Volodymyr V. Nekrashevych

Publication: Memoirs of the American Mathematical Society
Publication Year: 2015; Volume 237, Number 1122
ISBNs: 978-1-4704-1544-0 (print); 978-1-4704-2511-1 (online)
DOI: http://dx.doi.org/10.1090/memo/1122
Published electronically: February 16, 2015
Keywords:Hyperbolic groupoids, Smale spaces, Smale quasi-flows

View full volume PDF

View other years and numbers:

Table of Contents


Chapters

  • Introduction
  • Chapter 1. Technical preliminaries
  • Chapter 2. Preliminaries on groupoids and pseudogroups
  • Chapter 3. Hyperbolic groupoids
  • Chapter 4. Smale quasi-flows and duality
  • Chapter 5. Examples of hyperbolic groupoids and their duals

Abstract


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

References [Enhancements On Off] (What's this?)