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Geometric Group Theory

An Introduction

  • Clara Löh

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Clara Löh
    Pages 1-5
  3. Groups

    1. Front Matter
      Pages 7-7
    2. Clara Löh
      Pages 9-49
  4. Groups → Geometry

    1. Front Matter
      Pages 51-51
    2. Clara Löh
      Pages 53-74
    3. Clara Löh
      Pages 75-114
    4. Clara Löh
      Pages 115-163
  5. Geometry of groups

    1. Front Matter
      Pages 165-165
    2. Clara Löh
      Pages 167-202
    3. Clara Löh
      Pages 203-256
    4. Clara Löh
      Pages 257-287
    5. Clara Löh
      Pages 289-315
  6. Back Matter
    Pages 317-389

About this book

Introduction

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology.

Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability.

This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Keywords

MSC 2010 20F65 20F67 20F69 20F05 20F10 20E08 20E05 20E06 geometric group theory group actions and geometry quasi-isometry of groups Cayley graphs of groups rigidity in group theory curvature and fundamental groups hyperbolic groups negatively curved groups amenable groups growth of groups Gromov boundary

Authors and affiliations

  • Clara Löh
    • 1
  1. 1.Fakultät für MathematikUniversität Regensburg RegensburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-72254-2
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-72253-5
  • Online ISBN 978-3-319-72254-2
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site