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Noeuds - Knots



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Knots have been studied extensively by mathematicians for the last hundred years. Recently the study of knots has proved to be of great interest to theoretical physicists and molecular biologists. One of the most peculiar things which emerges as you study knots is how a category of objects as simple as a knot could be so rich in profound mathematical connections.
<http://www.c3.lanl.gov/mega-math/workbk/knot/knot.html> <http://www.earlham.edu/~peters/knotlink.htm>
David Eppstein, Theory Group, ICS, UC Irvine.
<http://www.ics.uci.edu/~eppstein/junkyard/knot.html> <http://www.flamingpear.com/knot.html>
Théorie du Noeud
<http://www.eetopologie.org/>
Slavik Jablan
<http://members.tripod.com/vismath5/bor/index.html>
mathematics of the unknot under tension
by Martin Probert
Many ethnographical string figures have come down to us only in the form of an ambiguous photograph in which, at the crossings, it is impossible to determine by eye which string lies over which. A knowledge of the set of all look-alikes ('similar-looking string figures') is a considerable aid in attempting to reconstruct such a figure.
<http://website.lineone.net/~m.p/sf/sfmaths1.html>

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PAGES PERSONNELLES - HOME PAGES

<http://www.math.uiowa.edu/~wu/> <http://www.math.s.kobe-u.ac.jp/HOME/nakanisi/index.html> <http://www-fourier.ujf-grenoble.fr/~lescop/>
thèse : invariants de Vassiliev
<http://spoirier.lautre.net/>
Vassiliev invariants and combinatorial structures
Lectures delivered at Graduate School of Mathematical Sciences University of Tokyo
<http://www.pdmi.ras.ru/~duzhin/Vics/>
On the Vassiliev Knot Invariants
<http://www.math.toronto.edu/~drorbn/papers/OnVassiliev/index.html>

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ANNEAUX - WEB RINGS

has been created to join Celtic and Pagan websites in an everlasting circle for those who seek the knowledge and magick of the Gods and Goddesses. The content of your site must be Celtic or Pagan in content. I do not accept sites that have racist, Satanic or XXX Adult related material.
<http://www.geocities.com/Athens/Acropolis/4717/celticknot.html>

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PROBLÈMES - PROBLEMS

Wall's k - The 4-move - The Grid Conjecture - The additivity issue - The X-moves
<http://guests.mpim-bonn.mpg.de/askitas/doc/conj.html>

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MATHEMATICA

<http://www.ma.huji.ac.il/~drorbn/papers/PDI/>

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LOGICIELS - SOFTWARES

Ying-Qing Wu - The MD energy is defined by J. Simon for polygonal knots. A polygonal knot K consists of several edges E_1, ..., E_n in the Euclidean space, which form a closed knotted loop. The ends of the edges are called the vertices of the knot. The energy contributed between E_i and E_j is (L_i)(L_j)/(D_ij*D_ij) where L_i is the length of E_i, and D_ij is the minimum distance between E_i and E_j. The energy of K is obtained by summing such contributions over all E_i and E_j which are not adjacent.
<http://www.math.uiowa.edu/~wu/min/ming.html> <http://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.html>
The Surface Evolver models the evolution of surfaces driven by various forces. Graphics can be output under a variety of formats on several different machines.
<http://www.geom.umn.edu/software/download/evolver.html>
KnotPlot requires both OpenGL and the OpenGL Utility Toolkit (GLUT) to be installed on your computer.
<http://www.pims.math.ca/knotplot/download.html>

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THÉORIE - THEORY

<http://library.thinkquest.org/12295/>

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THÈSES - THESIS

<http://www.cs.ubc.ca/nest/imager/contributions/scharein/thesis/thesis.html>

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LIVRES - BOOKS

<http://www.cs.ubc.ca/nest/imager/contributions/scharein/knot-theory/references.html>

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DOCUMENTS - PAPERS

<http://www.math.uiuc.edu/~jms/Papers/>
Ritzenthaler Christophe Mémoires des élèves de première année
<http://www.dptmaths.ens-cachan.fr/stages/9697/ritzenthaler.ps.gz>
Publications et prépublications  en liaison avec les tresses
<http://www.liafa.jussieu.fr/~picantin/GDRpub/index.html>
Luis Paris Institut de Mathématiques de Bourgogne
Le GDR TRESSES existe depuis 8 ans. Il a été créé par Patrick Dehornoy et regroupait à son origine des équipes travaillant sur les aspects algébriques, algorithmiques et/ou topologiques des groupes de tresses, ainsi que sur tout ce qui y est relié. Depuis 4 ans, sous la direction de Christian Blanchet, le GDR s?est orienté un peu plus vers la topologie de basse dimension, les invariants quantiques, la TQFT et l?homologie de Khovanov, tout en développant de nouveaux thèmes qui lui sont originaux tels que les groupes de Garside.
<http://math.u-bourgogne.fr/IMB/tresses/index>
The braid order: history and connection with knots. Etc.
<http://www.math.unicaen.fr/~dehornoy/>
Vaughan F.R. Jones ?
<http://math.berkeley.edu/~vfr/jones.pdf>

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JOURNAUX - LETTERS

Rachel Nowak, Melbourne NewScientist.com news service. The knotty problem of choosing the optimum way of lacing up shoes has been solved by a new mathematical proof... Burkard Polster, of Monash University in Melbourne, Australia, used combinatorial mathematics to come up with his proof. This branch of maths is used to solve a huge variety of problems, including resource allocation and finding the best ways to lay chips in a computer.
<http://www.newscientist.com/news/news.jsp?id=ns99993136>

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HISTORIQUES - HISTORY

Born: 31 Dec 1952 in Gisborne, New Zealand
In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology. As a result, he found a new polynomial invariant for knots and links in 3-space. His invariant had been missed completely by topologists, in spite of intense activity in closely related areas during the preceding 60 years, and it was a complete surprise.
<http://www-gap.dcs.st-and.ac.uk/%7ehistory/Mathematicians/Jones_Vaughan.html>

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ARTS

<http://www.wallace.net/knots/samples/> <http://galifrey.triode.net.au/Maths/Knots/knots.html>

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LIENS - LINKS

<liens_math.html> <http://www.earlham.edu/~peters/knotlink.htm#knot theory> <http://www.cs.ubc.ca/nest/imager/contributions/scharein/various/OtherLinks.html>

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