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Universitext

Geometric Group Theory

An Introduction

Authors: Löh, Clara

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  • Features more than 250 exercises of varying difficulty including programming tasks
  • Introduces the key notions from quasi-geometry, such as growth, hyperbolicity, boundary constructions and amenability
  • Assumes only a basic background in group theory, metric spaces and point-set topology
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  • ISBN 978-3-319-72254-2
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About this Textbook

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.

About the authors

Clara Löh is Professor of Mathematics at the University of Regensburg, Germany. Her research focuses on the interaction between geometric topology, geometric group theory, and measurable group theory. This includes cohomological, geometric, and combinatorial methods. 

Reviews

“The structure of the chapters can make the reader independent, thus the book can be used ‘outside of the classroom’ for self-teaching by both young researchers and experienced scholars. The book is well written … . it is ready to fill a gap in the literature for such an interesting and active branch of mathematics.” (Dimitrios Varsos, zbMATH 1426.20001, 2020)

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $69.99
price for USA in USD
  • ISBN 978-3-319-72254-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Group Theory
Book Subtitle
An Introduction
Authors
Series Title
Universitext
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-72254-2
DOI
10.1007/978-3-319-72254-2
Softcover ISBN
978-3-319-72253-5
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XI, 389
Number of Illustrations
19 b/w illustrations, 100 illustrations in colour
Topics

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