The mystery of knots
Subtitle: computer programming for knot tabulation
By: Charilaos N. Aneziris.
Series: K & E series on knots and everything ;; v. 20
Publisher: World Scientific
Published: 1999
Place of publication: Singapore; River Edge, NJ
Language: eng
Number of pages: 396
Subjects: Knot theory.; Knot theory -- Statistical methods.; Nœuds, Théorie des.; Nœuds, Théorie des -- Méthodes statistiques.
Notes: Includes bibliographical references (p. 383-387) and index.
Table of contents: title: Pt. 1. A Knot Theory Primer. 1. A General Understanding of Topology. 2. Knot Theory as a Branch of Topology. 3. The Regular Presentations of Knots. 4. The Equivalence Moves. 5. The Knot Invariants. 6. Elements of Group Theory. 7. The Fundamental Group. 8. The Knot Group. 9. The Colorization Invariants. 10. The Alexander Polynomial. 11. The Theory of Linear Homogeneous Systems. 12. Calculating the Alexander Polynomial. 13. The "minor" Alexander Polynomials. 14. The Meridian-Longitude Invariants. 15. Proving a Knot's Chirality. 16. Braid Theory - Skein Invariants. 17. Calculating the HOMFLYPT Polynomials. 18. Knot Theory after the HOMFLYPT; title: Pt. 2. The Problem of Knot Tabulation. 1. Basic Concepts of Computer Programming. 2. The Dowker Notation. 3. Drawing the Knot. 4. When is a Notation Drawable? 5. The "Equal Drawability" Moves. 6. Multiple Notations for Equivalent Knots. 7. Ordering the Dowker Notations. 8. Calculating the Notation Invariants. 9. A Few Examples. 10. The Knot Tabulation Algorithm. 11. The Pseudocode. 12. The Flowchart. 13. Actual Results; title: Pt. 3. The Table of Knots.