Classical Topology and Combinatorial Group Theory Book

	Preface to the First Edition
	Preface to the Second Edition
Ch. 0	Introduction and Foundations	1
0.1	The Fundamental Concepts and Problems of Topology	2
0.2	Simplicial Complexes	19
0.3	The Jordan Curve Theorem	26
0.4	Algorithms	36
0.5	Combinatorial Group Theory	40
Ch. 1	Complex Analysis and Surface Topology	53
1.1	Riemann Surfaces	54
1.2	Nonorientable Surfaces	62
1.3	The Classification Theorem for Surfaces	69
1.4	Covering Surfaces	80
Ch. 2	Graphs and Free Groups	89
2.1	Realization of Free Groups by Graphs	90
2.2	Realization of Subgroups	99
Ch. 3	Foundations for the Fundamental Group	109
3.1	The Fundamental Group	110
3.2	The Fundamental Group of the Circle	116
3.3	Deformation Retracts	121
3.4	The Seifert-Van Kampen Theorem	124
3.5	Direct Products	132
Ch. 4	Fundamental Groups of Complexes	135
4.1	Poincare's Method for Computing Presentations	136
4.2	Examples	141
4.3	Surface Complexes and Subgroup Theorems	156
Ch. 5	Homology Theory and Abelianization	169
5.1	Homology Theory	170
5.2	The Structure Theorem for Finitely Generated Abelian Groups	175
5.3	Abelianization	181
Ch. 6	Curves on Surfaces	185
6.1	Dehn's Algorithm	186
6.2	Simple Curves on Surfaces	190
6.3	Simplification of Simple Curves by Homeomorphisms	196
6.4	The Mapping Class Group of the Torus	206
Ch. 7	Knots and Braids	217
7.1	Dehn and Schreier's Analysis of the Torus Knot Groups	218
7.2	Cyclic Coverings	225
7.3	Braids	233
Ch. 8	Three-Dimensional Manifolds	241
8.1	Open Problems in Three-Dimensional Topology	242
8.2	Polyhedral Schemata	248
8.3	Heegaard Splittings	252
8.4	Surgery	263
8.5	Branched Coverings	270
Ch. 9	Unsolvable Problems	275
9.1	Computation	276
9.2	HNN Extensions	285
9.3	Unsolvable Problems in Group Theory	290
9.4	The Homeomorphism Problem	298
	Bibliography and Chronology	307
	Index	319