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Topic: Link (knot theory)

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NEW KNOT TABLES After Redmeister [4], all knot tables that can be found in knot theory books are simple copies of the first: sometimes, some projection is slightly changed, or turned upside down, and that's all. A prime knot or link with singular digons, expressed by a Conway symbol, is called generating, and a knot or link without digons is called a basic polyhedron [14,16,17]. Because the complete concept of new knot tables is based on the notion of generating knots and links and families originating from them, one of the possible future aims can be a search for new knot and link invariants that will be the invariants of families. members.tripod.com /vismath7/knotab

PlanetMath: knot theory A knot diagram is a projection of a link onto a plane such that no more than two points of the link are projected to the same point on the plane and at each such point it is indicated which strand is closest to the plane (usually by erasing part of the lower strand). Knot theory is the study of knots and links. This is version 5 of knot theory, born on 2002-12-19, modified 2003-01-29. planetmath.org /encyclopedia/KnotTheory.html   (959 words)

AMCA: KNOTS in Poland 2003: The mini-semester on Knot Theory and its Ramifications - List of Speakers KNOTS in Poland 2003: The mini-semester on Knot Theory and its Ramifications Joao Faria Martins Knot Theory with the Quantum Lorentz Group Alexander Mednykh Hyperbolic volumes of knot and link cone manifolds at.yorku.ca /cgi-bin/amca/calg-01   (959 words)

Knot Theory Knots and links; diagrams; simple examples; ambient and planar isotopy; Reidemeister moves and theorem; number of link components as a simple invariant; signs of oriented crossings; the writhe of a knot. Knot theory has many relations to topology, physics, and (more recently!) even the study of the structure of DNA. This is an introductory course in Knot Theory. www.math.ucla.edu /~radko/191.1.05w   (959 words)

AMCA: KNOTS in WASHINGTON 10 Japan-USA; workshop in Knot Theory - List of Speakers KNOTS in WASHINGTON 10 Japan-USA; workshop in Knot Theory Seiichi Kamada Abstract link diagrams and virtual knots Kazuko Onda A characterization of knots in a spatial graph at.yorku.ca /c/a/e/a/01.htm   (959 words)

Chronological list of videos Ghrist & SU(n) invariants via Yokata and link-component reversing for the HOMFLY polynomial W.B.R. Lickorish Combinatorial Problems Arising in Knots and 3-manifolds #3/4 970121-970122 Wheels, Wheeling and the Kontsevich integral of the unknot Dror Bar Natan & Legendrian and the traverse knots in tight contact structures S. Tabachnikov Combinatorial Problems Arising in Knots and 3-manifolds #2/4 970121 MSRI Geometry Workshop, 1992 Combinatorics and low-dimensional topology X-S Lin & Homology and combinatorics of singular knots V. Gordon--Introductory Workshop in Combinatorics and Low-dimensional topology #18/20 960812-960823 Representation theory and symmetric functions, V B. www.msri.org /local/library/video_list.html   (959 words)

NEW KNOT TABLES A prime knot or link with singular digons, expressed by a Conway symbol, is called generating, and a knot or link without digons is called a basic polyhedron [14,16,17]. Because the complete concept of new knot tables is based on the notion of generating knots and links and families originating from them, one of the possible future aims can be a search for new knot and link invariants that will be the invariants of families. After Redmeister [4], all knot tables that can be found in knot theory books are simple copies of the first: sometimes, some projection is slightly changed, or turned upside down, and that's all. members.tripod.com /vismath7/knotab   (1879 words)

NEW KNOT TABLES A prime knot or link with singular digons, expressed by a Conway symbol, is called generating, and a knot or link without digons is called a basic polyhedron [14,16,17]. Because the complete concept of new knot tables is based on the notion of generating knots and links and families originating from them, one of the possible future aims can be a search for new knot and link invariants that will be the invariants of families. After Redmeister [4], all knot tables that can be found in knot theory books are simple copies of the first: sometimes, some projection is slightly changed, or turned upside down, and that's all. www.mi.sanu.ac.yu /~jablans/knotab   (1879 words)

PlanetMath: knot theory Knot theory is the study of knots and links. A knot diagram is a projection of a link onto a plane such that no more than two points of the link are projected to the same point on the plane and at each such point it is indicated which strand is closest to the plane (usually by erasing part of the lower strand). Luckily the knot theorist is not usually interested in the exact form of a knot or link, but rather the in its equivalence class. planetmath.org /encyclopedia/KnotTheory.html   (954 words)

Proceedings of the American Mathematical Society Y. Miyazawa, Vassiliev's invariant and link polynomials (in Japanese), Teijigen-Tayotai no Toporojii to Musubime-riron (Topology of Low-dimensional Manifolds and Knot Theory), Proceedings of Research Institute for Mathematics and Computer Science, vol. Taizo Kanenobu, Vassiliev-type invariants of a theta-curve, J. Knot Theory Ramifications 6 (1997), 455-477. V.A. Vassiliev, Cohomology of knot spaces, Theory of Singularities and Its Applications (V.I. Arnold, ed.), Advances in Soviet Math., vol. www.ams.org /proc/1996-124-12/S0002-9939-96-03628-3/home.html   (328 words)

Preprint Page for Stuart Rankin Knot Theory Work of Ortho Flint and Stuart Rankin In the first paper in the list, we introduce four operators on knots and show that, when used according to very simple rules on the prime alternating knots of n crossings, the set of all prime alternating knots of n+1 crossings is obtained. The master array can be used to construct an ideal knot configuration for a prime alternating knot, by which we mean that two prime alternating knots, each in their ideal configuration, are equivalent if and only if they are identical. www.math.uwo.ca /~srankin/knotprint.html   (328 words)

Knot theory Syllabus MA3F2 Knots and links through their diagrams, orientation, positive and negative crossings, writhe of a diagram, linking numbers, Reidemeister moves, regular isotopy and isotopy, Hopf not isotopic to Whitehead. Alexander polynomials, defined as the determinant of an arc labelling, effects of mirrors and reverses, vanishing on a splittable link, knot sums, reef and granny knots, behaviour of Alexander polynomial under sum of knots. Knot colouring, labelling arcs with integers, colouring mod n, splittable links, Borromean rings, chess board structure on a diagram, reduced connected diagram determines quadrilateral decomposition, crossing equations sum to 0. www.maths.warwick.ac.uk /~bjs/Syllabus_98_99.html   (328 words)

NEW KNOT TABLES A prime knot or link with singular digons, expressed by a Conway symbol, is called generating, and a knot or link without digons is called a basic polyhedron [14,16,17]. Because the complete concept of new knot tables is based on the notion of generating knots and links and families originating from them, one of the possible future aims can be a search for new knot and link invariants that will be the invariants of families. After Redmeister [4], all knot tables that can be found in knot theory books are simple copies of the first: sometimes, some projection is slightly changed, or turned upside down, and that's all. www.mi.sanu.ac.yu /~jablans/knotab   (1879 words)

Preprint Page for Stuart Rankin Knot Theory Work of Ortho Flint and Stuart Rankin It is shown that one may choose any prime alternating link diagram of a given minimal crossing size and by applications of just two operators (namely T and OTS) to the selected seed link, one obtains all prime alternating link diagrams of the desired minimal crossing size. In the first paper in the list, we introduce four operators on knots and show that, when used according to very simple rules on the prime alternating knots of n crossings, the set of all prime alternating knots of n+1 crossings is obtained. www.math.uwo.ca /~srankin/knotprint.html   (1080 words)

Knot Theory Knot theory studies the placement of one-dimensional objects called strings [23,24,25] in a three-dimensional space. As the parameters of the flow are varied the components of this link, the knots, may collapse to points (Hopf bifurcations) or coalesce (saddle-node or pitchfork bifurcations). Classification of knots  and links is a fundamental problem in topology. www.drchaos.net /drchaos/Book/node141.html   (552 words)

DMS.MPS.a9504832.txt Knot theory--the study of aspects of the geometry of knots and links which are insensitive to continuous deformations--has always had a lot to give to, and take from, the qualitative side of the theory of equations. Mathematically, a rich source of knots is the theory of equations in a small number of variables (the simplest mathematical link, which looks like two rings in a piece of chain, comes from the simple equation xy = 0). Other work in progress includes development of skein theory for Legendrian knots, an attack on a question of Harer about fibered links (are they all stably Hopf-plumbed?), and (with Michel Boileau) a study of Stein-fillable 3-manifolds. www.cs.utexas.edu /users/yguan/NSFAbstracts/Abstracts/MPS/DMS.MPS.a9504832.txt   (552 words)

m363.html Course Description: An introduction to the mathematical theory of knots and links, with emphasis on the modern combinatorial methods. An Introduction to Knot Theory, by W. Raymond Lickorish, Springer-Verlag; Knot Theory and its Applications, by Kunio Murasugi, Birkhauser; Knots and Physics and Knots and Applications, written/edited by Louis Kauffman and published by World Scientific. Among specific topics to be covered are: Reidemeister moves on link projections, ambient and regular isotopies, linking number, tricolorability, rational tangles, braids, torus knots, seifert surfaces and genus, the knot polynomials (bracket, X, Jones, Alexander, HOMFLY), crossing numbers of alternating knots and amphicheirality. www.cwru.edu /artsci/math/langer/courses/m363.html   (497 words)

Louis Kauffman, Abstract In this generalization of classical knot theory, many new phenomena appear: There are non-trivial knots with trivial Jones polynomial.There are non-trivial knots with non-trivial Jones polynonmial, but with the infinite cyclic fundamental group. In virtual knot theory we study Gauss codes representing "knots" that have an abstract existence, but require virtual crossings when one tries to draw them in the plane. Virtual Knot theory is to classical knot theory as graphs are to planar graphs. www.math.binghamton.edu /dept/topsem/00Abstracts/kauff2000.html   (150 words)

m363.html Course Description: An introduction to the mathematical theory of knots and links, with emphasis on the modern combinatorial methods. An Introduction to Knot Theory, by W. Raymond Lickorish, Springer-Verlag; Knot Theory and its Applications, by Kunio Murasugi, Birkhauser; Knots and Physics and Knots and Applications, written/edited by Louis Kauffman and published by World Scientific. Among specific topics to be covered are: Reidemeister moves on link projections, ambient and regular isotopies, linking number, tricolorability, rational tangles, braids, torus knots, seifert surfaces and genus, the knot polynomials (bracket, X, Jones, Alexander, HOMFLY), crossing numbers of alternating knots and amphicheirality. www.cwru.edu /artsci/math/langer/courses/m363.html   (150 words)

PlanetMath: knot theory Knot theory is the study of knots and links. A knot diagram is a projection of a link onto a plane such that no more than two points of the link are projected to the same point on the plane and at each such point it is indicated which strand is closest to the plane (usually by erasing part of the lower strand). This is version 5 of knot theory, born on 2002-12-19, modified 2003-01-29. planetmath.org /encyclopedia/KnotTheory.html   (150 words)

PlanetMath: knot theory Knot theory is the study of knots and links. A knot diagram is a projection of a link onto a plane such that no more than two points of the link are projected to the same point on the plane and at each such point it is indicated which strand is closest to the plane (usually by erasing part of the lower strand). This is version 5 of knot theory, born on 2002-12-19, modified 2003-01-29. planetmath.org /encyclopedia/KnotTheory.html   (150 words)

Citebase - Whitney towers and the Kontsevich integral [1] D Bar-Natan, Vassiliev homotopy string link invariants, J. Knot Theory Ramications 4 (1995) 13-32 MR1321289 We use the finite type theory to show that our invariants agree with the (leading term of the tree part of the) Kontsevich integral in the case where the 4-manifold is obtained from the 4-ball by attaching handles along a link in the 3-sphere. We continue to develop an obstruction theory for embedding 2-spheres into 4-manifolds in terms of Whitney towers. www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0401441   (828 words)

Tangle Decompositions Of Double Torus Knots And Links - Ozawa (ResearchIndex) Ozawa, Tangle decompositions of double torus knots and links, to appear in J. Knot Theory and its Ramification. Introduction A knot or link L is said to be double torus if L is contained in a genus two Heegaard surface of S 3. Journal of Knot Theory and Its Ramifications World Scientific Publishing... citeseer.ist.psu.edu /302509.html   (828 words)

1 If a lawyer can do research in knot theory, it can't be that hard.) Unforunately, there are many knots with equivalent Alexander polynomial that can be shown to be isotopically different through the uses of other invariants. In the vernacular of the knot theorist, a knot determines its complement. But for knots a seminal result of Cameron Gordon and John Luecke showed that two knot are homeomorphic if and only if they are isotopic. www.math.buffalo.edu /~menasco/Knottheory.html   (1176 words)

Knots in Washington 3 Knot and link diagrams are usually drawn on the plane or on the two-sphere. Here we regard combinatorial knot theory as a theory of planar knot diagrams The topic of this talk is new, and it yields a chance to examine knot home.gwu.edu /~przytyck/knots/kw3.html   (1176 words)

Knot Theory Online - The Web Site for Learning More about Mathematical Knot Theory Knots on the Web*** - The most complete and exhaustive collection of links to every site you can imagine on knot tying, knot theory, knot art, knot software, knot books, and even a knot gallery for reference and enjoyment. Knot Theory page for tons of information on the subject. If you have a knot site you'd like to add, please feel free to email mrpayne@freelearning.com with your site name, and please feel free to link to our site and activities. www.freelearning.com /knots/fun.htm   (1122 words)

The Geometry Junkyard: Knot Theory There is of course an enormous body of work on knot invariants, the 3-manifold topology of knot complements, connections between knot theory and statistical mechanics, etc. I am instead interested here primarily in geometric questions arising from knot embeddings. Atlas of oriented knots and links, Corinne Cerf extends previous lists of all small knots and links, to allow each component of the link to be marked by an orientation. Connections between knot theory and dissection of hyperbolic polyhedra. www.ics.uci.edu /~eppstein/junkyard/knot.html   (673 words)

KNOTS In [KH] we define the coloring number of a knot or link K to be the least number of colors (greater than 1) needed to color it in the 2b-a fashion for any diagram of K. It is a nice exercise to verify that the coloring number of the figure eight knot is indeed four. This essay constitutes an introduction to the theory of knots as it has been influenced by developments concurrent with the discovery of the Jones polynomial in 1984 and the subsequent explosion of research that followed this signal event in the mathematics of the twentieth century. The Alexander polynomial is an algebraic modulus for the knot. www.math.uic.edu /~kauffman/Tots/Knots.htm   (673 words)

Skein relation - Wikipedia, the free encyclopedia Depending on the knot polynomial in question, the links (or tangles) appearing in a skein relation may be oriented or unoriented. Skein relations occur in knot theory, where they are most often used to give a simple definition of a knot polynomial. To recursively define a knot (link) polynomial, a function F is fixed and for any triple of diagrams and their polynomials labelled as above, en.wikipedia.org /wiki/Skein_relation   (538 words)

Knot Theory Knot theory studies the placement of one-dimensional objects called strings [23,24,25] in a three-dimensional space. In the chaotic regime, this link is extraordinarily complex, consisting of an infinite number of periodic orbits (knots). Classification of knots  and links is a fundamental problem in topology. www.drchaos.net /drchaos/Book/node141.html   (552 words)

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