Benjamin Fine

Gerhard Rosenberger

Anja Moldenhauer

Leonard Wienke

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.

Nielsen Methods, Covering Spaces, and Hyperbolic Groups

Topics in Infinite Group Theory

Annika Schürenberg

Fundamentals of mathematics are presented in the two-volume set in an exciting and pedagogically sound way. The present volume examines the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history. New: A chapter on discrete Morse theory and still more graph theory for solving further classical problems as the Travelling Salesman and Postman problem.

Leonard Wienke

Books

Your next favorite book is out there