Table of Contents

A Knot Theory Primer

• An Introduction to Knot Theory
• Showing Knot Equivalence
• Showing Knot Inequivalence
• An Introduction to Braid Theory
• The Knot Group
• The "Color Tests"
• The Alexander-Conway Polynomial
• The other Alexander Polynomials
• The HOMFLYPT polynomial
• Non-Linear Color Tests

The Problem of Knot Classification

• Denoting Regular Knot projections
• Denoting Regular Knot projections, the Sequel
• When is a notation drawable?
• Equal Drawability
• Identifying Equivalent Knot Projections
• Ordering Knot Notations
• Connected Sums
• Comparing Regular Knot Projections
• Results for Various NF
• Calculating the Alexander polynomials
• Obtaining the other Alexander polynomials
• The Knot Table
• The list with knots and their invariants (up to 12 crossings)
• The computer output file for 12 crossing knots
• Knots on a Cubic Lattice
• The Closed Self-Avoiding Walk (SAW) Notation
• Equivalence moves

The Problem of the Tabulation of Links

• What do KNOTS and LINKS have in common?
• Vive la Difference!
• How good is the Link Notation?
• The Challenges
• Who is thy neighbor?
• To draw or not to draw...
• Different Notations - Identical Presentations
• Ordering the Links
• "New" Link Invariants
• Prime Links
• Link Tabulation Algorithm
• List of Links
• Colorization Invariants - Component Number / Link Number
• Colorization Invariants - S(3) Group
• Colorization Invariants - S(4) Group
• Colorization Invariants - S(5) Group
• Colorization Invariants - S(6) Group
• Colorization Invariants - S(7) Group
• Colorization Invariants - S(9) Group
• Showing that the links are non-trivial
• Are the links prime?
• Proving that the links cannot be decomposed

This is the latest addition to this online tutorial. Its goal is to extend the discussion from the study of knots to the study of links.

You may be interested in my published book, The Mystery of Knots

Charilaos Aneziris

charilaos_aneziris@standardandpoors.com

Copyright 1995, 2001

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