Home > Science > Math > Topology > Knot Theory
Knots, braids, tangles: papers, software and pictures.
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.
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.
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.
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.
http://www.math.uiowa.edu/~jsimon/aaron.html
Some results and figures from Aaron Trautwein's thesis.
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.
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.
http://mathworld.wolfram.com/topics/KnotTheory.html
An overview of knot theory from Mathworld
https://www.liverpool.ac.uk/~su14/knotgroup.html
Links to preprints and to programs written in pascal for doing knot calculations.
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.
http://www.math.utk.edu/~morwen/knotscape.html
By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
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.
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.
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.
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.
http://www.ics.uci.edu/~eppstein/junkyard/knot.html
A page of links on geometric questions arising from knot embeddings.
http://www.knotplot.com/
A visual exploration of mathematical 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''.
http://www.ams.org/notices/199505/sumners.pdf
Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy.
http://mathworld.wolfram.com/KnotPolynomial.html
Some knot invariants.
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