Geometric Group Theory

An Introduction

Clara Löh

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English

Springer International Publishing AG
19 January 2018

Groups & group theory; Non-Euclidean geometry; Differential & Riemannian geometry; Topology; Combinatorics & graph theory

Series: Universitext

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.

By: Clara Löh
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2017
Dimensions: Height: 235mm, Width: 155mm,
Weight: 829g
ISBN: 9783319722535
ISBN 10: 3319722530
Series: Universitext
Pages: 389
Publication Date: 19 January 2018
Audience: College/higher education , A / AS level
Format: Paperback
Publisher's Status: Active

1 Introduction.- Part I Groups.- 2 Generating groups.- Part II Groups > Geometry.- 3 Cayley graphs.- 4 Group actions.- 5 Quasi-isometry.- Part III Geometry of groups.- 6 Growth types of groups.- 7 Hyperbolic groups.- 8 Ends and boundaries.- 9 Amenable groups.- Part IV Reference material.- A Appendix.- Bibliography.- Indices.

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 for Geometric Group Theory: An Introduction

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)