Book:Colin C. Adams/The Knot Book

From ProofWiki
Jump to: navigation, search

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

Published $1994$, 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