Topological Methods in Group Theory (Graduate Texts in Mathematics) 〈Vol. 243〉

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Topological Methods in Group Theory (Graduate Texts in Mathematics) 〈Vol. 243〉

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  • 製本 Hardcover:ハードカバー版/ページ数 475 p./サイズ 41 illus.
  • 商品コード 9780387746111

基本説明

Features - Covers important topics not covered elsewhere, such as cell trading; Provides an accessible review of general topology; Contains nearly 50 figures; Includes exercises throughout each chapter; Self-contained and suitable for a graduate course on algebraic topology.

Full Description

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.

Contents

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.