Topological Methods in Group Theory Hardcover - 2007 - 2008th Edition
by Ross Geoghegan
From the rear cover
Topological Methods in Group Theory is about the interplay between algebraic topology and the theory of infinite discrete groups. The author has kept three kinds of readers in mind: graduate students who have had an introductory course in algebraic topology and who need a bridge from common knowledge to the current research literature in geometric, combinatorial and homological group theory; group theorists who would like to know more about the topological side of their subject but who have been too long away from topology; and manifold topologists, both high- and low-dimensional, since the book contains much basic material on proper homotopy and locally finite homology not easily found elsewhere.
The book focuses on two main themes:
1. Topological Finiteness Properties of groups (generalizing the classical notions of "finitely generated" and "finitely presented");
2. Asymptotic Aspects of Infinite Groups (generalizing the classical notion of "the number of ends of a group").
Illustrative examples treated in some detail include: Bass-Serre theory, Coxeter groups, Thompson groups, Whitehead's contractible 3-manifold, Davis's exotic contractible manifolds in dimensions greater than three, the Bestvina-Brady Theorem, and the Bieri-Neumann-Strebel invariant. The book also includes a highly geometrical treatment of Poincar duality (via cells and dual cells) to bring out the topological meaning of Poincar duality groups.
To keep the length reasonable and the focus clear, it is assumed that the reader knows or can easily learn the necessary algebra (which is clearly summarized) but wants to see the topology done in detail. Apart from the introductory material, most of the mathematics presented here has not appeared in book form before.
Details
- Title Topological Methods in Group Theory
- Author Ross Geoghegan
- Binding Hardcover
- Edition number 2008th
- Edition 2008
- Pages 473
- Volumes 1
- Language ENG
- Publisher Springer
- Date 2007-12-17
- Illustrated Yes
- Features Bibliography, Illustrated, Index
- ISBN 9780387746111 / 0387746110
- Weight 1.76 lbs (0.80 kg)
- Dimensions 9.26 x 6.46 x 1.05 in (23.52 x 16.41 x 2.67 cm)
- Library of Congress subjects Group theory, Discrete groups
- Library of Congress Catalog Number 2007940952
- Dewey Decimal Code 510
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Topological Methods in Group Theory (Graduate Texts in Mathematics, 243)
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