Topics in Infinite Group Theory

This book offers an advanced exploration of infinite group theory, focusing on the interplay between combinatorial and geometric approaches. It covers Nielsen methods, covering spaces, fundamental groups, and hyperbolic groups.

Topics in Infinite Group Theory provides an in-depth exploration of various aspects of infinite group theory, serving as both an advanced overview and a rigorous introduction to combinatorial and geometric group theory. The author emphasizes the interplay between these two significant areas, offering a unique perspective on their relationship. Throughout the book, several theorems are demonstrated multiple times using different methods, showcasing both purely combinatorial and purely geometric approaches, as well as hybrid arguments that draw from both fields.

The first section of the book is dedicated to Nielsen methods, which lay the groundwork for understanding the subsequent topics. This part introduces key results and examples that are essential for grasping the more complex concepts that follow. By establishing a solid foundation, the author prepares readers for a deeper dive into the intricacies of group theory.

In the subsequent sections, the focus shifts to covering spaces and fundamental groups, where the author presents covering space proofs of various group theoretic results. The final part of the book delves into the theory of hyperbolic groups, further enriching the reader's understanding of infinite group theory. Throughout the text, prominent examples are used to illustrate the concepts, and the author provides insights into both solved and unsolved problems in the field, making this book a valuable resource for anyone looking to deepen their knowledge of infinite group theory.