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Knot Theory

Science > Math > Topology > Knot Theory

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Research Oriented (7)

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	Knot Theory - http://mathworld.wolfram.com/topics/KnotTheory.html An overview of knot theory from Mathworld
	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.
	Knot Plot - http://www.pims.math.ca/knotplot/ 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.
	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.
	Megamath Knot Theory Page - http://www.c3.lanl.gov/mega-math/gloss/knots/knots.html An introductory overview of knot theory.

	Knotscape - http://www.math.utk.edu/~morwen/knotscape.html By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
	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''.
	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 Knot Theory Home Page - http://library.thinkquest.org/12295/ Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.
	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.

	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.
	Mathematics and Knots Exhibition - http://www.bangor.ac.uk/cpm/exhib/ High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory.
	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.
	Harmonic Knots - http://www.carthage.edu/~trautwn/ An introduction to harmonic knots. Gives (parametric) formulas for knots of up to 7 crossings.
	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.

	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.
	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.
	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.maths.warwick.ac.uk/~bjs/MA3F2-page.html Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.
	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.

	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.
	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.
	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.
	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.

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