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Knot Theory


Knot Theory
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A Circular History of Knot Theory open in new window
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.
(http://www.math.buffalo.edu/~menasco/Knottheory.html)

A Knot Theory Primer open in new window
Comprehensive knot theory site focusing on the knot classification problem and knot tabulations. Has a tabulation of knots with up to 12 crossings.
(http://www.inst.bnl.gov/~wei/contents.html)

A Third Year Lecture Course on Knots open in new window
Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.
(http://www.maths.warwick.ac.uk/~bjs/MA3F2-page.html)

BraidLink open in new window
Braidlink is software for knot and braid theory computations. It performs both analytic and numerical manipulations of knots and braids.
(http://www.knot-theory.org/)

Cook's Borromean Ring Links open in new window
Links to pages and two outlines of proofs that show the Borromean rings can't be made from circular rings.
(http://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Bo)

Geometry and the Imagination open in new window
Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.
(http://math.dartmouth.edu/~doyle/docs/gi/gi/gi.html)

Harmonic Knots open in new window
An introduction to harmonic knots. Gives (parametric) formulas for knots of up to 7 crossings.
(http://www.carthage.edu/~trautwn/)

History of Knot Theory open in new window
Biographies of early knot theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson.
(http://www.maths.ed.ac.uk/~aar/knots/index.htm)

Kauffman, Louis H open in new window
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.
(http://bilbo.math.uic.edu/~kauffman/)

Knot Plot open in new window
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.
(http://www.pims.math.ca/knotplot/)

Knot Theory open in new window
An overview of knot theory from Mathworld
(http://mathworld.wolfram.com/topics/KnotTheory.html)

Knot Theory open in new window
Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations.
(http://www.mapleapps.com/categories/mathematics/Knot%20theor)

Knot Theory Group University of Liverpool open in new window
Links to preprints and to programs written in pascal for doing knot calculations.
(http://www.liv.ac.uk/PureMaths/MIN_SET/CONTENT/RESEARCH_GROU)

Knot Theory Invariants: The HOMFLY Polynomial open in new window
A brief article on the HOMFLY polynomial and how it is calculated.
(http://library.thinkquest.org/12295/data/Invariants/Articles)

Knot Theory Online open in new window
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.
(http://www.freelearning.com/knots/)

Knots on the Web (Peter Suber) open in new window
The most comprehensive collection of knotting resources on the web. Sections on knot tying, mathematical knot theory, knot art, and knot books.
(http://www.earlham.edu/~peters/knotlink.htm)

Knotscape open in new window
By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
(http://www.math.utk.edu/~morwen/knotscape.html)

Mathematics and Knots Exhibition open in new window
High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory.
(http://www.bangor.ac.uk/cpm/exhib/)

Megamath Knot Theory Page open in new window
An introductory overview of knot theory.
(http://www.c3.lanl.gov/mega-math/gloss/knots/knots.html)

Morwen Thistlethwaite's Home Page open in new window
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.
(http://www.math.utk.edu/~morwen/)

Pictures of Knots open in new window
A table of graphics of all knots of up to nine crossings. Also includes pictures of some links.
(http://www.math.unl.edu/~mbritten/ldt/table9.gif)

String Figure Mathematics (or Trivial Knot Theory) open in new window
A mathematical analysis of string figures. Theorems, examples, illustrations and conjectures on patterns created with an unknotted string.
(http://website.lineone.net/~m.p/sf/menu.html)

The Geometry Junkyard: Knot Theory open in new window
A page of links on geometric questions arising from knot embeddings.
(http://www.ics.uci.edu/~eppstein/junkyard/knot.html)

The Knot Theory Home Page open in new window
Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.
(http://library.thinkquest.org/12295/main.html)

The KnotPlot Site open in new window
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.
(http://www.cs.ubc.ca/labs/imager/contributions/scharein/Knot)

Thomas Fink (Tie Knots) open in new window
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''.
(http://www.tcm.phy.cam.ac.uk/~tmf20/)

Using Topology to Probe the Hidden Action of Enzymes open in new window
Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy (in pdf format).
(http://www.ams.org/notices/199505/sumners.pdf)


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