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Home: Science: Math: Topology: Knot Theory

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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.
http://www.math.buffalo.edu/~menasco/Knottheory.html
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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.
http://www.inst.bnl.gov/~wei/contents.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

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.
http://www.warwick.ac.uk/~maaac/MA3F2-page.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

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.
http://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Geometry and the Imagination
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
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Harmonic Knots
Some results and figures from Aaron Trautwein's thesis.
http://www.math.uiowa.edu/~jsimon/aaron.html
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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.
http://www.maths.ed.ac.uk/~aar/knots/index.htm
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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.
http://www.math.uic.edu/~kauffman/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Knot Theory
An overview of knot theory from Mathworld
http://mathworld.wolfram.com/topics/KnotTheory.html
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Knot Theory Group University of Liverpool
Links to preprints and to programs written in pascal for doing knot calculations.
http://www.liv.ac.uk/~su14/knotgroup.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Knot Theory Invariants: The HOMFLY Polynomial
A brief article on the HOMFLY polynomial and how it is calculated.
http://library.thinkquest.org/12295/data/Invariants/Articles/HOMFLY.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

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.
http://www.earlham.edu/~peters/knotlink.htm
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Knotscape
By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
http://www.math.utk.edu/~morwen/knotscape.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Mathematics and Knots
An exhibition of knots provided by the Division of Mathematics, University of Wales, Bangor.
http://www.popmath.org.uk/exhib/knotexhib.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Megamath Knot Theory Page
An introductory overview of knot theory.
http://www.c3.lanl.gov/mega-math/gloss/knots/knots.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

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.
http://www.math.utk.edu/~morwen/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

New Knot Tables
Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos.
http://members.tripod.com/vismath7/knotab/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Pictures of Knots
A table of graphics of all knots of up to nine crossings. Also includes pictures of some links.
http://www.math.unl.edu/~mbrittenham2/ldt/table9.gif
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

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.
http://website.lineone.net/~m.p/sf/menu.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

The Geometry Junkyard: Knot Theory
A page of links on geometric questions arising from knot embeddings.
http://www.ics.uci.edu/~eppstein/junkyard/knot.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

The Knot Theory Home Page
Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.
http://library.thinkquest.org/12295/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

The KnotPlot Site
A visual exploration of mathematical knots.
http://www.knotplot.com/
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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''.
http://www.tcm.phy.cam.ac.uk/~tmf20/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

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.
http://www.ams.org/notices/199505/sumners.pdf
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Wolfram MathWorld: Knot Polynomial
Some knot invariants.
http://mathworld.wolfram.com/KnotPolynomial.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

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