Science: Math: Topology: Knot_Theory

 Research Oriented  (8)

Knots on the Web (Peter Suber)
- The most comprehensive 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.

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.

The Geometry Junkyard: Knot Theory
A page of links on geometric questions arising from knot embeddings.

Harmonic Knots
An introduction to harmonic knots. Gives (parametric) formulas for knots of up to 7 crossings.

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.

Knot Plot
A collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a program to visualize and manipulate mathematical knots in three and four dimensions.

Knot Theory
An overview of knot theory from Mathworld

Knot Theory
Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations.

Knot Theory Group University of Liverpool
Links to preprints and to programs written in pascal for doing knot calculations.

Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.

Knot Theory Invariants: The HOMFLY Polynomial
A brief article on the HOMFLY polynomial and how it is calculated.

Knot Theory Online
This site is designed for mathematics students at the high school and college levels as an introduction to an area of mathematics seldom explored in the typical math classroom - the Theory of Knots.

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.

The KnotPlot Site
Has a large number of beautiful graphics of knots created with KnotPlot. Contains an introductory section on mathematical knot theory. KnotPlot software for various platfroms can be downloaded.

Knotscape
By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.

Mathematics and Knots Exhibition
High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory.

Megamath Knot Theory Page
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.

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.

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.

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 (in pdf format).

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