viii Content s
Chapter 3
Invariants of Knots 5 7
3.1 Unknottin g Number 5 7
3.2 Bridg e Number 6 4
3.3 Crossin g Number 6 7
Chapter 4
Surfaces and Knots 7 1
4.1 Surface s without Boundary 7 1
4.2 Surface s with Boundary 8 7
4.3 Genu s and Seifert Surfaces 9 5
Chapter 5
Types of Knots 107
5.1 Toru s Knots 107
5.2 Satellit e Knots 115
5.3 Hyperboli c Knots 119
5.4 Braid s 127
5.5 Almos t Alternating Knots 139
Chapter 6
Polynomials 147
6.1 Th e Bracket Polynomial and the Jones Polynomial 147
6.2 Polynomial s of Alternating Knots 156
6.3 Th e Alexander and HOMFLY Polynomials 165
6.4 Amphicheiralit y 176
Chapter/
Biology, Chemistry and Physics 181
7.1 DN A 181
7.2 Synthesi s of Knotted Molecules 195
7.3 Chiralit y of Molecules 20 1
7.4 Statistica l Mechanics and Knots 20 5
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