Overview

This is a well-balanced introduction to topology that stresses geometric aspects. Focusing on historical background and visual interpretation of results, it emphasizes spaces with few dimensions, where visualization is possible, and interaction with combinatorial group theory via the fundamental group. It also present algorithms for topological problems. Most of the results and proofs are known, but some have been simplified or placed in a new perspective. Over 300 illustrations, many interesting exercises, and challenging open problems are included. New in this edition is a chapter on unsolvable problems, which includes the first textbook proof that the main problem of topology, the homeomorphism problem, is unsolvable.

Full Product Details

Author:   John Stillwell
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2nd ed. 1993
Volume:   72
Dimensions:   Width: 15.60cm , Height: 2.00cm , Length: 23.40cm
Weight:   1.480kg
ISBN:  

9780387979700

ISBN 10:   0387979700
Pages:   336
Publication Date:   25 March 1993
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

0 Introduction and Foundations.- 0.1 The Fundamental Concepts and Problems of Topology.- 0.2 Simplicial Complexes.- 0.3 The Jordan Curve Theorem.- 0.4 Algorithms.- 0.5 Combinatorial Group Theory.- 1 Complex Analysis and Surface Topology.- 1.1 Riemann Surfaces.- 1.2 Nonorientable Surfaces.- 1.3 The Classification Theorem for Surfaces.- 1.4 Covering Surfaces.- 2 Graphs and Free Groups.- 2.1 Realization of Free Groups by Graphs.- 2.2 Realization of Subgroups.- 3 Foundations for the Fundamental Group.- 3.1 The Fundamental Group.- 3.2 The Fundamental Group of the Circle.- 3.3 Deformation Retracts.- 3.4 The Seifert—Van Kampen Theorem.- 3.5 Direct Products.- 4 Fundamental Groups of Complexes.- 4.1 Poincaré’s Method for Computing Presentations.- 4.2 Examples.- 4.3 Surface Complexes and Subgroup Theorems.- 5 Homology Theory and Abelianization.- 5.1 Homology Theory.- 5.2 The Structure Theorem for Finitely Generated Abelian Groups.- 5.3 Abelianization.- 6 Curves on Surfaces.- 6.1 Dehn’s Algorithm.- 6.2 Simple Curves on Surfaces.- 6.3 Simplification of Simple Curves by Homeomorphisms.- 6.4 The Mapping Class Group of the Torus.- 7 Knots and Braids.- 7.1 Dehn and Schreier’s Analysis of the Torus Knot Groups.- 7.2 Cyclic Coverings.- 7.3 Braids.- 8 Three-Dimensional Manifolds.- 8.1 Open Problems in Three-Dimensional Topology.- 8.2 Polyhedral Schemata.- 8.3 Heegaard Splittings.- 8.4 Surgery.- 8.5 Branched Coverings.- 9 Unsolvable Problems.- 9.1 Computation.- 9.2 HNN Extensions.- 9.3 Unsolvable Problems in Group Theory.- 9.4 The Homeomorphism Problem.- Bibliography and Chronology.

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