Does the Jones Polynomial Detect Unknottedness?  
   Research paper (in postscript format) showing that any knot with trivial Jones polynomial must have at least 18 crossings. The number of different Alexander, Homfly and Jones polynomials for knots of up to 15 crossings is given.
   http://www.informatik.hu-berlin.de/~hougardy/paper/abs_does.html

A Dynamic Approach to Calculating the HOMFLY Polynomial for Directed Knots and Links  
   A research paper describing an algorithm for calculating the HOMFLY polynomial of directed knots and links. The algorithm has a better time bound for large links than algorithns that ignore duplicates. Source code is on the site.
   http://burtleburtle.net/bob/knot/thesis.html

Knots in Braid Notation  
   Listing of every knot of up to 11 crossings in braid notation. Useful for computer calculations in knot theory.
   http://www.scoriton.demon.co.uk/knots.html

Liverpool University Knot Theory Group  
   Articles and preprints from 1987 onward. Some are available for download in postscript format.
   http://www.liv.ac.uk/~su14/knotprints.html

Knot Theory and Quantum Gravity  
   Quantizing general relativity brings knot theory into quantum gravity. The Jones polynomial is shown to give rise to physical states of quantum gravity. Links to research papers by the author.
   http://www.phys.lsu.edu/faculty/pullin

Mark Brittenham's Papers and Preprints  
   Research papers on three manifolds, foliations, surgery on knots.
   http://www.math.unl.edu/~mbritten/personal/pprdescr.html#perseif

Knot Polynomials  
   Research paper on a state-space representation of the HOMFLY polynomial, by B. Bollobás, L. Pebody and D. Weinreich. Links to the paper in pdf,dvi and ps formats.
   http://www.gettysburg.edu/~dweinrei/research/homfly.html