Classical Topology and Combinatorial Group Theory: v. 72

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.

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0: Introduction and Foundations. 1: Complex Analysis and Surface Topology. 2: Graphs and Free Groups. 3: Foundations for the Fundamental Group. 4: Fundamental Groups of Complexes. 5: Homology Theory and Abelianization. 6: Curves on Surfaces. 7: Knots and Braids. 8: Three-Dimensional Manifolds. 9: Unsolvable Problems.

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