Coarse geometry of topological groups / Christian Rosendal.

Format:

Book

Author/Creator:

Rosendal, Christian, author.

Series:

Cambridge tracts in mathematics ; 223.

Cambridge tracts in mathematics ; 223

Language:

English

Subjects (All):

Geometric group theory.

Topological groups.

Transformation groups.

Polish spaces (Mathematics).

Physical Description:

ix, 297 pages : illustrations ; 24 cm.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2021.

Summary:

"This book provides a general framework for doing geometric group theory for many non-locally-compact topological transformation groups that arise in mathematical practice, including homeomorphism and diffeomorphism groups of manifolds, isometry groups of separable metric spaces and automorphism groups of countable structures. Using Roe's framework of coarse structures and spaces, the author defines a natural coarse geometric structure on all topological groups. This structure is accessible to investigation, especially in the case of Polish groups, and often has an explicit description, generalising well-known structures in several familiar cases such as finitely generated discrete groups, compactly generated locally compact groups and Banach spaces. In most cases, the coarse geometric structure is metrisable and may even be refined to a canonical quasimetric structure on the group. The book contains plenty of worked examples and sufficient introductory material to be accessible to beginning graduate students. An appendix outlines several open problems in this young and rich theory"-- Provided by publisher.

Contents:

Coarse structure and metrisability

Structure theory

Sections, cocycles and group extensions

Polish groups of bounded geometry

Automorphism groups of countable structures

Zappa-Szép products.

Notes:

Includes bibliographical references and index.

Other Format:

Online version: Rosendal, Christian. Coarse geometry of topological groups

ISBN:

9781108842471

110884247X

OCLC:

1243012855