Open Directory - Science: Math: Topology: Knot Theory
See also: - A collection of knotting resources on the web. Sections on knot tying, mathematical knot theory, knot art, and knot books. - 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. - Comprehensive knot theory site focusing on the knot classification problem and knot tabulations. Has a tabulation of knots with up to 12 crossings. - Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids. - Links to pages and two outlines of proofs that show the Borromean rings can't be made from circular rings. - 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. - Biographies of early knot theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson. - 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 - Links to preprints and to programs written in pascal for doing knot calculations. - 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. - An exhibition of knots provided by the Division of Mathematics, University of Wales, Bangor. - An introductory overview of knot theory. - 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. - Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos. - A table of graphics of all knots of up to nine crossings. Also includes pictures of some links. - A mathematical analysis of string figures. Theorems, examples, illustrations and conjectures on patterns created with an unknotted string. - A page of links on geometric questions arising from knot embeddings. - Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations. - A visual exploration of mathematical 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''. - Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy. [PDF] - Some knot invariants.
