Topological Methods in Group Theory
Published on 29. November 2010
Book
Paperback/Softback
XVI, 473 pages
978-1-4419-2564-0 (ISBN)
Description
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.
Reviews / Votes
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)More details
Series
Edition
Softcover reprint of hardcover 1st ed. 2008
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
41 s/w Abbildungen
XVI, 473 p. 41 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 27 mm
Weight
739 gr
ISBN-13
978-1-4419-2564-0 (9781441925640)
DOI
10.1007/978-0-387-74614-2
Schweitzer Classification
Other editions
Additional editions
Ross Geoghegan
Topological Methods in Group Theory
E-Book
12/2007
1st Edition
Springer
€69.54
Available for download
Ross Geoghegan
Topological Methods in Group Theory
Book
12/2007
Springer
€96.29
Shipment within 5-7 days
Person
Matthias Beck received his initial training in mathematics in Würzburg, Germany, received his Ph.D. in mathematics from Temple University, and is now associate professor of mathematics at San Francisco State University. He is the recipient of the 2013 MAA Haimo Award for Distinguished College or University Teaching of Mathematics. He is the author of a previously published Springer book, Computing the Continuous Discretely (with Sinai Robins).
Ross Geoghegan received his initial training in mathematics in Dublin, Ireland, received his Ph.D. in mathematics from Cornell University, and is now professor of mathematics at the State University of New York at Binghamton. He is the author of a previously published Springer book, Topological Methods in Group Theory.
Content
Algebraic Topology for Group Theory.- CW Complexes and Homotopy.- Cellular Homology.- Fundamental Group and Tietze Transformation.- Some Techniques in Homotopy Theory.- Elementary Geometric Topology.- Finiteness Properties of Groups.- The Borel Construction and Bass-Serre Theory.- Topological Finiteness Properties and Dimension of Groups.- Homological Finiteness Properties of Groups.- Finiteness Properties of Some Important Groups.- Locally Finite Algebraic Topology for Group Theory.- Locally Finite CW Complexes and Proper Homotopy.- Locally Finite Homology.- Cohomology of CW Complexes.- Topics in the Cohomology of Infinite Groups.- Cohomology of Groups and Ends of Covering Spaces.- Filtered Ends of Pairs of Groups.- Poincaré Duality in Manifolds and Groups.- Homotopical Group Theory.- The Fundamental Group At Infinity.- Higher homotopy theory of groups.- Three Essays.- Three Essays.