# Book:Colin C. Adams/The Knot Book

Jump to navigation
Jump to search
## Colin C. Adams:

## 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

### 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*