Book:Colin C. Adams/The Knot Book

Colin C. Adams: The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots

Published $\text {1994}$, W.H. Freeman and Company

ISBN 0-7167-4219-5

Subject Matter

• Knot Theory

Contents

Preface

Chapter 1: Introduction

1.1 Introduction

1.2 Composition of Knots

1.3 Reidemeister Moves

1.4 Links

1.5 Tricolorability

1.6 Knots and Sticks

Chapter 2: Tabulating Knots

2.1 History of Knot Tabulation

2.2 The Dowker Notation for Knots

2.3 Conway's Notation

2.4 Knots and Planar Graphs

Chapter 3: Invariants of Knots

3.1 Unknotting Number

3.2 Bridge Number

3.3 Crossing Number

Chapter 4: Surfaces and Knots

4.1 Surfaces without Boundary

4.2 Surfaces with Boundary

4.3 Genus and Seifert Surfaces

Chapter 5: Types of Knots

5.1 Torus Knots

5.2 Satellite Knots

5.3 Hyperbolic Knots

5.4 Braids

5.5 Almost Alternating Knots

Chapter 6: Polynomials

6.1 The Bracket Polynomial and the Jones Polynomial

6.2 Polynomials of Alternating Knots

6.3 The Alexander and HOMFLY Polynomials

6.4 Amphicheirality

Chapter 7: Biology, Chemistry, and Physics

7.1 DNA

7.2 Synthesis of Knotted Molecules

7.3 Chirality of Molecules

7.4 Statistical Mechanics and Knots

Chapter 8: Knots, Links, and Graphs

8.1 Links in Graphs

8.2 Knots in Graphs

8.3 Polynomials of Graphs

Chapter 9: Topology

9.1 Knot Complements and Three-Manifolds

9.2 The Three-Sphere and Lens Spaces

9.3 The Poincaré Conjecture, Dehn Surgery and the Gordon-Luecke Theorem

Chapter 13: Higher Dimensional Knotting

10.1 Picturing Four Dimensions

10.2 Knotted Spheres in Four Dimensions

10.3 Knotted Three-spheres in Five-space

Knot Jokes and Pastimes

Appendix Table of Knots, Links, and Knot and Link Invariants

Suggested Readings and References

Index