Overview
- 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
Part of the book series: Universitext (UTX)
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Table of contents (9 chapters)
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Groups
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Groups → Geometry
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Geometry of groups
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
About this book
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.
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Bibliographic Information
Book Title: Geometric Group Theory
Book Subtitle: An Introduction
Authors: Clara Löh
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-72254-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-72253-5Published: 19 January 2018
eBook ISBN: 978-3-319-72254-2Published: 19 December 2017
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XI, 389
Number of Illustrations: 19 b/w illustrations, 100 illustrations in colour
Topics: Group Theory and Generalizations, Differential Geometry, Hyperbolic Geometry, Manifolds and Cell Complexes (incl. Diff.Topology), Graph Theory