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Knot Theory

Science > Math > Topology > Knot Theory

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A Circular History of Knot Theory - http://www.math.buffalo.edu/~menasco/Knottheory.html
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 - http://www.inst.bnl.gov/~wei/contents.html
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 - http://www.warwick.ac.uk/~maaac/MA3F2-page.html
Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.

Cook's Borromean Ring Links - http://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.html
Links to pages and two outlines of proofs that show the Borromean rings can't be made from circular rings.

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

History of Knot Theory - http://www.maths.ed.ac.uk/~aar/knots/index.htm
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 - http://www.math.uic.edu/~kauffman/
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 Theory - http://www.mapleapps.com/categories/mathematics/Knot%20theory/html/Knots.htm
Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations.

Knot Theory - http://mathworld.wolfram.com/topics/KnotTheory.html
An overview of knot theory from Mathworld

Knot Theory Group University of Liverpool - http://www.liv.ac.uk/~su14/knotgroup.html
Links to preprints and to programs written in pascal for doing knot calculations.

Knot Theory Invariants: The HOMFLY Polynomial - http://library.thinkquest.org/12295/data/Invariants/Articles/HOMFLY.html
A brief article on the HOMFLY polynomial and how it is calculated.

Knots on the Web (Peter Suber) - http://www.earlham.edu/~peters/knotlink.htm
A collection of knotting resources on the web. Sections on knot tying, mathematical knot theory, knot art, and knot books.

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

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

Morwen Thistlethwaite's Home Page - http://www.math.utk.edu/~morwen/
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 - http://members.tripod.com/vismath7/knotab/
Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos.

Pictures of Knots - http://www.math.unl.edu/~mbrittenham2/ldt/table9.gif
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) - http://website.lineone.net/~m.p/sf/menu.html
A mathematical analysis of string figures. Theorems, examples, illustrations and conjectures on patterns created with an unknotted string.

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

The Knot Theory Home Page - http://library.thinkquest.org/12295/
Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.

Thomas Fink (Tie Knots) - http://www.tcm.phy.cam.ac.uk/~tmf20/
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 - http://www.ams.org/notices/199505/sumners.pdf
Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy.

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