The knot book 0821836781, 1012214648, 1235090620, 1018326553, 1293285870, 1137077417, 9780821836781

Table of contents :
Cover......Page 1
Title......Page 2
Copyright......Page 5
Contents......Page 8
Preface......Page 12
Chapter 1 Introduction......Page 16
1.1 Introduction......Page 16
1.2 Composition of Knots......Page 22
1.3 Reidemeister Moves......Page 27
1.4 Links......Page 31
1.5 Tricolorability......Page 37
1.6 Knots and Sticks......Page 42
Chapter 2 Tabulating Knots......Page 46
2.1 History of Knot Tabulation......Page 46
2.2 The Dowker Notation for Knots......Page 50
2.3 Conway's Notation......Page 56
2.4 Knots and Planar Graphs......Page 66
Chapter 3 Invariants of Knots......Page 72
3.1 Unknotting Number......Page 72
3.2 Bridge Number......Page 79
3.3 Crossing Number......Page 82
Chapter 4 Surfaces and Knots......Page 86
4.1 Surfaces without Boundary......Page 86
4.2 Surfaces with Boundary......Page 102
4.3 Genus and Seifert Surfaces......Page 110
Chapter 5 Types of Knots......Page 122
5.1 Torus Knots......Page 122
5.2 Satellite Knots......Page 130
5.3 Hyperbolic Knots......Page 134
5.4 Braids......Page 142
5.5 Almost Alternating Knots......Page 154
Chapter 6 Polynomials......Page 162
6.1 The Bracket Polynomial and the Jones Polynomial......Page 162
6.2 Polynomials of Alternating Knots......Page 170
6.3 The Alexander and HOMFLY Polynomials......Page 180
6.4 Amphicheirality......Page 190
Chapter 7 Biology, Chemistry and Physics......Page 196
7.1 DNA......Page 196
7.2 Synthesis of Knotted Molecules......Page 210
7.3 Chirality of Molecules......Page 216
7.4 Statistical Mechanics and Knots......Page 220
Chapter 8 Knots, Links, and Graphs......Page 230
8.1 Links in Graphs......Page 230
8.2 Knots in Graphs......Page 237
8.3 Polynomials of Graphs......Page 246
Chapter 9 Topology......Page 258
9.1 Knot Complements and Three-Manifolds......Page 258
9.2 The Three-Sphere and Lens Spaces......Page 261
......Page 272
Chapter 10 Higher Dimensional Knotting......Page 280
10.1 Picturing Four Dimensions......Page 280
10.2 Knotted Spheres in Four Dimensions......Page 287
10.3 Knotted Three-Spheres in Five-Space......Page 288
Knot Jokes and Pastimes......Page 291
Appendix: Table of Knots, Links, and Knot and Link Invariants......Page 294
Suggested Readings and References......Page 306
Index......Page 318
A......Page 318
B......Page 318
C......Page 318
D......Page 319
E......Page 319
F......Page 319
G......Page 319
H......Page 319
I......Page 319
J......Page 320
K......Page 320
L......Page 320
M......Page 320
N......Page 320
O......Page 320
P......Page 320
R......Page 320
S......Page 320
T......Page 321
U......Page 321
V......Page 321
W......Page 321
X......Page 321
Y......Page 321
Z......Page 321
Corrections to the 2004 AMS Printing......Page 322
Back Cover......Page 323

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