Topological Methods in Group Theory

Springer Published(December 17, 2007) | PDF file(473 pages) | 3.74mb(rar size)

Topological Methods in Group Theory (Graduate Texts in Mathematics)/byRoss Geoghegan
Description
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 Poincaré
duality (via cells and dual cells) to bring out the topological meaning of Poincaré 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.


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