Directory of Knot Theory Resources

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Knots, braids, tangles: papers, software and pictures.

Subcategories

• Research Oriented

Resources in This Category

• 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 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.

• Harmonic Knots

  http://www.math.uiowa.edu/~jsimon/aaron.html
  Some results and figures from Aaron Trautwein's thesis.

• 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://mathworld.wolfram.com/topics/KnotTheory.html
  An overview of knot theory from Mathworld

• Knot Theory Group University of Liverpool

  https://www.liverpool.ac.uk/~su14/knotgroup.html
  Links to preprints and to programs written in pascal for doing knot calculations.

• 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.

• 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 KnotPlot Site

  http://www.knotplot.com/
  A visual exploration of mathematical knots.

• 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.

• Wolfram MathWorld: Knot Polynomial

  http://mathworld.wolfram.com/KnotPolynomial.html
  Some knot invariants.

Related Categories

• Home > Science > Math > Topology > Geometric Topology
• Home > Reference > Knots

 

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