Knot Theory

• Reference: Knots  (82)
• Science: Math: Topology: Geometric Topology  (6)

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.
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.
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.
Geometry and the Imagination :

- Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.
The Geometry Junkyard: Knot Theory :

- A page of links on geometric questions arising from knot embeddings.
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.
Knot Plot :

- 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.
Knot Theory :

- Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations.
Knot Theory :

- An overview of knot theory from Mathworld
Knot Theory Group University of Liverpool :

- Links to preprints and to programs written in pascal for doing knot calculations.
The Knot Theory Home Page :

- Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.
Knot Theory Invariants: The HOMFLY Polynomial :

- A brief article on the HOMFLY polynomial and how it is calculated.
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.
Knotscape :

- By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
Mathematics and Knots Exhibition :

- High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory.
Megamath Knot Theory Page :

- An introductory overview of knot theory.
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.
New Knot Tables :

- Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos.
Pictures of Knots :

- 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) :

- A mathematical analysis of string figures. Theorems, examples, illustrations and conjectures on patterns created with an unknotted string.
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.
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''.
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. [PDF]