Hyperbolic Groupoids and Duality
- ISBN-10
- 1470415445
- ISBN-13
- 9781470415440
- Category
- Duality theory (Mathematics)
- Pages
- 108
- Language
- English
- Published
- 2015-08-21
- Publisher
- American Mathematical Soc.
- Author
- Volodymyr Nekrashevych
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.
Get the book
Similar books
-
An Invitation to Quantum Groups and Duality: From Hopf Algebras to Multiplicative Unitaries and Beyond
By Thomas Timmermann[ 113 ] G . J . Murphy , C * - algebras and operator theory . Academic Press , Boston 1990 . ... [ 120 ] A . L . T . Paterson , Groupoids , inverse semigroups ... [ 121 ] G . K . Pedersen , C * - algebras and their automorphism groups .
-
Poincaré Duality Groups and Homology Manifolds
By James Andrew FowlerHowever, we also show that this is rather exceptional: uniform lattices in semisimple Lie groups which contain p-torsion (for p ≠ 2) do not act freely on Q -acyclic Q...
-
Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes
By Joseph Lipman, Leovigildo Alonso Tarrío, Ana Jeremías LópezGlobal Grothendieck Duality. Torsion sheaves. Duality for torsion sheaves. Flat base change. Consequences of the flat base change isomorphism. References 1. Preliminaries and main theorems. 10 30 42 47 58 70 85 89 First we need some ...