Book:Colin C. Adams/The Knot Book

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