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Open Directory - Science: Math: Topology: Knot Theory
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Knots on the Web (Peter Suber)
- A collection of knotting resources on the web. Sections on knot tying, mathematical knot theory, knot art, and knot books.
A Circular History of Knot Theory
- Starting with the flawed theory of Kelvin's knotted vortex to the work of Thurston, Jones and Witten, knot theory has circled back to its ancestral origins of theoretical physics.
A Knot Theory Primer
- Comprehensive knot theory site focusing on the knot classification problem and knot tabulations. Has a tabulation of knots with up to 12 crossings.
A Third Year Lecture Course on Knots
- Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.
Cook's Borromean Ring Links
- Links to pages and two outlines of proofs that show the Borromean rings can't be made from circular rings.
Geometry and the Imagination
- Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.
- Some results and figures from Aaron Trautwein's thesis.
History of Knot Theory
- Biographies of early knot theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson.
Kauffman, Louis H
- A topologist working in knot theory discusses the connection between knot theory and statistical mechanics. Sections on cybernetics and knots, Fourier knots and the author's research papers.
- An overview of knot theory from Mathworld
Knot Theory Group University of Liverpool
- Links to preprints and to programs written in pascal for doing knot calculations.
Knot Theory Invariants: The HOMFLY Polynomial
- A brief article on the HOMFLY polynomial and how it is calculated.
- By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
Mathematics and Knots
- An exhibition of knots provided by the Division of Mathematics, University of Wales, Bangor.
Megamath Knot Theory Page
- An introductory overview of knot theory.
Morwen Thistlethwaite's Home Page
- Has many beautiful images of symmetric knots, and information about a computer program called Knotscape (compiled binaries for Linux, Sunos and Alpha platforms). Includes pictures of knots with 13 crossings or less.
New Knot Tables
- Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos.
Pictures of Knots
- A table of graphics of all knots of up to nine crossings. Also includes pictures of some links.
String Figure Mathematics (or Trivial Knot Theory)
- A mathematical analysis of string figures. Theorems, examples, illustrations and conjectures on patterns created with an unknotted string.
The Geometry Junkyard: Knot Theory
- A page of links on geometric questions arising from knot embeddings.
The Knot Theory Home Page
- Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.
The KnotPlot Site
- A visual exploration of mathematical knots.
Thomas Fink (Tie Knots)
- Thomas Fink and Yong Mao, used ideas from statistical mechanics to show there are 85 ways to tie a tie. They discovered a number of new aesthetically pleasing tie knots. This page has links to their original papers and to their book ``The 85 Ways to Tie a Tie''.
Using Topology to Probe the Hidden Action of Enzymes
- Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy. [PDF]
Wolfram MathWorld: Knot Polynomial
- Some knot invariants.
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