From the reviews:„The author of this book has done a great service to the geometric group theory community by writing a very useful and well-written book on many topics in geometric group theory that every neophyte and researcher in the field should know. … This book is suitable as a textbook for a graduate course, with many good examples and exercises. The reviewer highly recommends this book as a basic reference book for topological methods in group theory.“ (John G. Ratcliffe, Mathematical Reviews, Issue 2008 j)„This is an interesting book on the interplay between algebraic topology and the theory of infinite discrete groups written for graduate students and group theorists who need to learn more in geometric and homological group theory. … It is a beautiful text in algebraic topology, with modern topics and which points the reader towards new research directions.“ (Corina Mohorianu, Zentralblatt MATH, Vol. 1142, 2008)“This book is an invaluable resource for anyone wanting a deep understanding of topics related to the ends of groups. … there is a good deal of material in this book that does not appear anywhere else in the literature. … Geoghegan’s book provides a well-presented, concrete development of geometric group theory focused on a topological approach.” (John Meier, Bulletin of the American Mathematical Society, July, 2012)
Aimed at advanced undergraduates and graduate students, this book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit. The author has included material which isn't covered in other textbooks. Much of the material will be of interest to group theorists who would like to know more about the topological side of their subject, as well as manifold topologists looking for basic material on proper homotopy and finite homology.
