Topological Methods in Group Theory
Springer-Verlag New York Inc.
978-0-387-74611-1 (ISBN)
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.
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.
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)
| Reihe/Serie | Graduate Texts in Mathematics ; 243 |
|---|---|
| Zusatzinfo | 41 Illustrations, black and white; XVI, 473 p. 41 illus. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-387-74611-0 / 0387746110 |
| ISBN-13 | 978-0-387-74611-1 / 9780387746111 |
| Zustand | Neuware |
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