Knot Theory Topology Math

Knot Theory

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

• Top/Reference/Knots
• Top/Science/Math/Topology/Geometric Topology

• - 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
  
• - Biographies of early knot theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson.
  
• - Links to preprints and to programs written in pascal for doing knot calculations.
  
• - Comprehensive knot theory site focusing on the knot classification problem and knot tabulations. Has a tabulation of knots with up to 12 crossings.
  
• - Has a large number of beautiful graphics of knots created with KnotPlot. Contains an introductory section on mathematical knot theory. KnotPlot software for various platfroms can be downloaded.
  
• - By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
  
• - High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory.
  
• - 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.
  
• - 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.
  
• - Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations.
  
• - A table of graphics of all knots of up to nine crossings. Also includes pictures of some links.
  
• - A mathematical analysis of string figures. Theorems, examples, illustrations and conjectures on patterns created with an unknotted string.
  
• - 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.
  
• - 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.
  
• - An introductory overview of knot theory.
  
• - Links to pages and two outlines of proofs that show the Borromean rings can't be made from circular rings.
  
• - A page of links on geometric questions arising from knot embeddings.
  
• - A brief article on the HOMFLY polynomial and how it is calculated.
  
• - Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos.
  
• - Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.
  
• - This site is designed for mathematics students at the high school and college levels as an introduction to an area of mathematics seldom explored in the typical math classroom - the Theory of Knots.
  
• - Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.
  
• - Braidlink is software for knot and braid theory computations. It performs both analytic and numerical manipulations of knots and braids.
  
• - An introduction to harmonic knots. Gives (parametric) formulas for knots of up to 7 crossings.
  
• - Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.
  
• - Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy (in pdf format).
  
  

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