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Katolog > Science > Math > Topology > Knot Theory > Research Oriented


Advanced aspects of knot theory [technical papers, etc].
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Links:

A Dynamic Approach to Calculating the HOMFLY Polynomial for Directed Knots and Links http://burtleburtle.net/bob/knot/thesis.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.
burtleburtle.net/bob/knot/thesis.html
Knots in Braid Notation http://www.scoriton.demon.co.uk/knots.html

Knots in Braid Notation

Listing of every knot of up to 11 crossings in braid notation. Useful for computer calculations in knot theory.
www.scoriton.demon.co.uk/knots.html
Liverpool University Knot Theory Group http://www.liv.ac.uk/~su14/knotprints.html

Liverpool University Knot Theory Group

Articles and preprints from 1987 onward. Some are available for download in postscript format.
www.liv.ac.uk/~su14/knotprints.html
Knot Theory and Quantum Gravity http://www.phys.lsu.edu/faculty/pullin

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.
www.phys.lsu.edu/faculty/pullin
Mark Brittenham's Papers and Preprints http://www.math.unl.edu/~mbritten/personal/pprdescr.html#perseif

Mark Brittenham's Papers and Preprints

Research papers on three manifolds, foliations, surgery on knots.
www.math.unl.edu/~mbritten/personal/pprdescr.html#perseif
Papers on Knot Theory at arxiv.org. http://arXiv.org/find/math/1/fr:+knot/0/1/0/past,all/0/1

Papers on Knot Theory at arxiv.org.

Search for papers held at LANL with the word 'knot' in them.
arXiv.org/find/math/1/fr:+knot/0/1/0/past,all/0/1
Knot Polynomials http://www.gettysburg.edu/~dweinrei/research/homfly.html

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.
www.gettysburg.edu/~dweinrei/research/homfly.html

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