Topics in Infinite Group Theory: Nielsen Methods, Covering Spaces, and Hyperbolic Groups

Benjamin Fine; Anja Moldenhauer; Gerhard Rosenberger; Leonard Wienke

Published by De Gruyter 2021

Topics in Infinite Group Theory

Nielsen Methods, Covering Spaces, and Hyperbolic Groups

Benjamin Fine , Anja Moldenhauer , Gerhard Rosenberger and Leonard Wienke

In the series De Gruyter STEM

https://doi.org/10.1515/9783110673371

Overview
Contents

About this book

This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives.

The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems.

Special emphasis is given to hyperbolic geodesic metric spaces and quasi isometries.
Includes applications for group amalgams and one-relator groups.
Discusses properties and examples of hyperbolic groups aiming at current research problems.

Author / Editor information

B. Fine, Fairfield University, USA; A. Moldenhauer, StatSoft Europe GmbH; G. Rosenberger, Uni. Hamburg; L. Wienke, Uni. Bremen, Germany.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Contents Publicly Available Download PDF	VII
1 Nielsen Methods Requires Authentication Unlicensed Licensed Download PDF	1
2 Covering Spaces Requires Authentication Unlicensed Licensed Download PDF	177
3 Hyperbolic Groups Requires Authentication Unlicensed Licensed Download PDF	233
Bibliography Requires Authentication Unlicensed Licensed Download PDF	369
Index Requires Authentication Unlicensed Licensed Download PDF	379

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Advanced Mathematics students and early-career researchers in Algebra and Group Theory.
Pages
- Front matter: 10
- Main content: 382
Illustrations
- Illustrations: 112
Keywords: Nielsen methods; Hyperbolic groups; Covering spaces

eBook

Published: August 23, 2021
ISBN: 9783110673371

Paperback

Published: August 23, 2021
ISBN: 9783110673340