Classical Topology and Combinatorial Group Theory

✍ Scribed by Dr. John Stillwell (auth.)

• Publisher: Springer US
• Year: 1980
• Tongue: English
• Leaves: 346
• Series: Graduate Texts in Mathematics 72
• Edition: 2nd
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction and Foundations....Pages 1-51
Complex Analysis and Surface Topology....Pages 53-88
Graphs and Free Groups....Pages 89-107
Foundations for the Fundamental Group....Pages 109-134
Fundamental Groups of Complexes....Pages 135-167
Homology Theory and Abelianization....Pages 169-184
Curves on Surfaces....Pages 185-215
Knots and Braids....Pages 217-240
Three-Dimensional Manifolds....Pages 241-274
Back Matter....Pages 275-304

✦ Subjects

Topology; Group Theory and Generalizations