41. Classical Knot Theory Classical knot theory. Epiphany Term 2003. Lecturer Dr C. Kearton. I shall distribute copies of the lecture notes and problem sheet at the first lecture. http://maths.dur.ac.uk/~dma0ck/gradtop.html

Classical Knot Theory Epiphany Term 2003 Lecturer: Dr C. Kearton I shall distribute copies of the lecture notes and problem sheet at the first lecture. If you want one before that, come and see me. Course material Format Lecture Notes Postscript PDF Problem Sheet Postscript PDF Problem Sheet with (some) solutions Postscript PDF Course Description Postscript PDF Software: GSview (viewer for Postcript files) Adobe Acrobat Reader (viewer for PDF files) Return to page top Recommended Books: See the lecture notes. Return to page top Links: e-mail to me. Durham Pure Mathematics Home page (formal page). Durham Pure Mathematicians' page (intended for members of the department but open to all). Department of Mathematical Sciences home page The University of Durham home page application/x-dvi; xdvi %s application/postscript; ghostview %s (or similar) to your .mailcap file. Info on HTML etc. NCSAA Beginner's Guide to HTML Computing Information for the Dept. of Mathematical Sciences - homepages University of Durham - ITS - About the Internet A Quick Review of HTML 3.0 ... Hypertext Markup Language - 2.0 - The HTML Coded Character Set

42. 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. http://www.maths.ed.ac.uk/~aar/knots/index.htm

HISTORY OF KNOT THEORY This home page is devoted to the history of knot theory, and is maintained by Jozef Przytycki and Andrew Ranicki. Our e-mail addresses are a.ranicki@edinburgh.ac.uk and przytyck@math.gwu.edu Please email to either of us any suggestions of additional material. BIOGRAPHIES OF EARLY KNOT THEORISTS Links to biographical entries in St. Andrews Mathematics History Archive M.Dehn P.Heegaard T.P.Kirkman J.B.Listing ... W.Wirtinger BIBLIOGRAPHY OF P.G.TAIT Provisional Bibliography prepared by Chris Pritchard, July, 2001 EARLY PAPERS ON KNOT THEORY A.Cayley, On a problem of arrangements, Proc. Royal Soc. Edinburgh, Vol. 9, 98 (1876-7), 338-342 Crum Brown, On a case of interlacing surfaces, Proc. Royal Soc. Edinburgh, Vol. 13, 121 (1885-6), 382-386 M.G.Haseman On knots, with a census of the amphicheirals with twelve crossings Trans. Roy. Soc. Edinburgh, 52 (1917-8), 235-255 also Ph.D thesis, Bryn Mawr College, 1918 M.G.Haseman Amphicheiral knots Trans. Roy. Soc. Edinburgh 52 (1919-20), 597-602. T.P.Kirkman

43. Links To Low-dimensional Topology: Knot Theory knot theory 3manifolds Miscellany. knot theory. Joe Christy lists. The page of the knot theory Group at the Univ. of Liverpool. An http://www.math.unl.edu/~mbritten/ldt/knots.html

General Conferences Pages of Links 3-manifolds ... Home pages Knot Theory Joe Christy has put together www.computop.org , to serve as a source for the computational 3-dimensional topology community. The site includes links to downloadable software, and a set of mailing lists. The page of the Knot Theory Group at the Univ. of Liverpool. An introduction to knot theory which seems to be aimed at teachers of mathematics can be found at Los Alamos National Laboratory There is also another knot theory page at the University of British Columbia. Another page , developed from a course for liberal arts students, is at York Univ. A discussion, and several lists, concerning the classification of knots, may be found in Charilaos Aneziris' home page. This table of knots up to nine crossings came from Sean Collom 's home page at Oxford. A collection of pages on Mathematics and Knots at the University of Wales. A huge page of links to pages on knots and knot theory of all kinds. An on knot theory appears in the November 1997 issue of American Scientist A page at the Univ. of Liverpool for accessing preprints on knot theory.

44. Knot Theory -- From MathWorld knot theory. The mathematical study of knots. Knot search. Eric W. Weisstein. knot theory. From MathWorldA Wolfram Web Resource. http http://mathworld.wolfram.com/KnotTheory.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Topology Knot Theory General Knot Theory ... Budney Knot Theory The mathematical study of knots . Knot theory considers questions such as the following: 1. Given a tangled loop of string, is it really knotted or can it, with enough ingenuity and/or luck, be untangled without having to cut it? 2. More generally, given two tangled loops of string, when are they deformable into each other? 3. Is there an effective algorithm (or any algorithm to speak of) to make these determinations? Although there has been almost explosive growth in the number of important results proved since the discovery of the Jones polynomial , there are still many "knotty" problems and conjectures whose answers remain unknown. Knot Link search Eric W. Weisstein. "Knot Theory." From

45. Knot Theory Resources knot theory resources. Recommended References. see index for total category for your convenience Best Retirement Spots Teacher http://futuresedge.org/mathematics/Knot_Theory.html

Knot Theory resources. Recommended References. [see index for total category] for your convenience: Best Retirement Spots Web Hosting ULTRAToolBox Resources on Diet and Nutrition Pain Relief Allergies Tech Refresh , and finally - a must check - Mediterranean diet Discovery. Knot Theory applications, theory, research, exams, history, handbooks and much more Introduction: Knot Book: An Elementary Introduction to Mathematical Theory of Knots by Colin C. Adams Introduction to Knot Theory by H. R. Crowell The Mathematical Theory of Knots and Braids: An Introduction by Siegfried Moran An Introduction to Knot Theory (Graduate Texts in Mathematics, 175) by W. B. Raymond Lickorish The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots by Colin C. Adams Applications: Theory: Knot Theory (Carus Mathematical Monographs, No 24) by Charles Livingston Knot Book: An Elementary Introduction to Mathematical Theory of Knots by Colin C. Adams Gauge Fields, Knots, and Gravity (Series on Knots and Everything, Vol. 4) by John C. Baez On Knots. (AM-115)

46. Knot Theory knot theory. knotting index; knot index; alternating knots; Celtic knots; Hyperbolic knot; Intro to knot theory; knots; knot theory; Forensic knot analysis. http://www-math.cudenver.edu/~jstarret/knots.html

Knot Theory A knot is an embedding of S1 in S3 (a 1-sphere in a 3-sphere, or a circle in three space plus the point at infinity), and a link is a disjoint collection of knots. We generally think of a link as being a set of interlocking rings, such as a chain, but here we include unlinked sets, and the rings comprising them can be knotted. A periodic orbit of a continuous time dynamical system with two degrees of freedom is a knot since it is a closed loop embedded in three space. A subset of the set of periodic orbits of a system forms a linkin other words, the periodic orbits may be tangled up with each other in complex and interesting ways. Chaotic dynamical systems are especially interesting from a knot theoretic point of view, as they have an infnite set of unstable periodic orbits that may be tangled in a way that includes every possible type of knot. There are many ways to characterize knots and links that may be used to characterize the orbits of dynamical systems. Among these are the polynomial invariants: Alexander Polynomial Conway Polynomial Jones Polynomial HOMFLYPT Polynomial Suppose we have chaotic time series data from a black box and we want to determine the equations of the underlying dynamics in the box. We may reconstruct the phase space of the experimental system from its time series by the method of time delay embedding and extract the periodic orbits. With a few periodic orbits in hand, we may be able to characterize the dynamics of the system from the polynomial invariants of the knots and links that are the periodic orbits.

47. The KnotPlot Site Has a large number of beautiful graphics of knots created with KnotPlot. Contains an introductory section on mathematical knot theory. KnotPlot software for various platfroms can be downloaded. http://www.cs.ubc.ca/labs/imager/contributions/scharein/KnotPlot.html

The KnotPlot Site Welcome to the KnotPlot Site! Here you will find a collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions. You can download KnotPlot and try it on your computer (see the link below), but first you may want to look at some of the images in the picture gallery. Also, have a browse through the Guestbook or sign it yourself Knot Pictures Check out the mathematical knots M ) page as well to see more knot pictures. Or try some of the following examples to see some knots in a different light. The pages marked with have been updated or created as of 11 Feb 2003. Those marked with an M have at least one MPEG animation. Various Collections The KnotServer (experimental, still not too useful), : 3D interactive viewer (which can save 3D models). Knots as radiating tubes M More knots as radiating tubes Fancy Knots and Links, together with Antoine's Necklace (a fractal link) Decorative knots: on white on black goth Ashley knots ... Nifty Knots with Fancy Lighting A knot zoo or two , and assortments of torus knots with neat colours knot chains , and knotted graphs More torus knots and links , arranged by crossing number Brunnian Links M Tangle Calculator Examples Linking Spheres in three or more dimensions PDF and PostScript examples Knot Carpets Celtic Knots 3D Stereoscopic Pictures ( page 1 page 2 page 3 page 4 ... Hopf Torus M

48. Mathematics And Knots Exhibition High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory. http://www.bangor.ac.uk/cpm/exhib/

An Exhibition Presented by the School of Mathematics of the University of Wales, Bangor: John Robinson Rhythm of Life Designed by : Ronnie Brown Nick Gilbert Tim Porter W.W.W. Production : Cara Quinton Sponsored by The London Mathematical Society CONTENTS Mathematics and Knots, University of Wales, Bangor, 1996. This material may be used freely for educational, artistic and scientific purposes, with acknowledgement, but may not be used for commercial purposes, for profit or in texts without the permission of the publishers. Link to Review of the Exhibition Borrowing the exhibition Why study Mathematics? Studying mathematics at Bangor ... Knots on the web visitors since April 21, 1998.

49. Menasco's Home Page Menasco s knot theory Hot List. Check out the following knot theory web sites. KnotPlot. A Circular History of knot theory. Knot Table courtesy of KnotPlot. http://www.math.buffalo.edu/~menasco/knot-theory.html

Menasco's Knot Theory Hot List Check out the following knot theory web sites. KnotPlot Knot Theory version 3.6 Snappea A Circular History of Knot Theory Knot Table courtesy of KnotPlot

50. Knot Theory On WWW knot theory on WWW. Japanese Books on knot theory. ?. ? , RH.?, RH. ? http://home.hiroshima-u.ac.jp/teragai/knot.html

Home Knot Theory on WWW Links to Personal Pages Profile Diary Tips on TeX ... Odd Man Out Knot Theory on WWW Knot2000(K2K) (Computer Aided Knot Theory) Knot Theory Visualization Kebap 3D The 3rd Japan-Mexico Joint Meeting on Topology and its Applications (December 6-10, 2004, Oaxaca, Mexico) Knots in Vancouver (July 19-23, 2004, PIMS, UBC, Canada) ... Journal of Knot Theory and its Ramifications Japanese Books on Knot Theory uŒ‹‚Ñ–Ú—˜_“ü–åv uŒ‹‚Ñ–Ú—˜_ŠTàv uŒ‹‚іڂ̐”Šwv uŒ‹‚Ñ–Ú—˜_‚Æ‚»‚̉ž—pv uŒ‹‚Ñ–Ú—˜_v C ‰Í“à–¾•v(•Ò’˜)CƒVƒ ƒvƒŠƒ“ƒK[ƒtƒFƒAƒ‰[ƒN“Œ‹žC1990”N uŒ‹‚Ñ–Ú—˜_“ü–åv C —é–ؐWˆê(’˜)CƒTƒCƒGƒ“ƒXŽÐC1991”N uŒ‹‚іڂ̐”Šw‚Æ•¨—v C ¬—шêÍ(’˜)C’©‘q‘“XC1992”N uƒRƒ“ƒsƒ [ƒ^‚É‚æ‚錋‚Ñ–Ú—˜_“ü–åv C —Ž‡–LsCŽR“cCŽiC–L“c‰p”üŽq(’˜)C–q–쏑“XC1996”N u‚RŽŸŒ³‘½—l‘Ì“ü–åv uŒ‹‚Ñ–Ú‚Æ—ÊŽqŒQv C ‘ºã‡(’˜)C’©‘q‘“XC2000”N uŒ‹‚Ñ–Ú‚Æ“Œv—ÍŠwv C˜a’BŽOŽ÷i’˜jCŠâ”g‘“XC2002”N u—ÊŽq•s•Ï—ʁv uüŒ`‘㐔‚©‚çƒzƒ‚ƒƒW[‚ցv uƒ‚ƒUƒCƒN‚Æ‚RŽŸŒ³‘½—l‘́v C J.M. ƒ‚ƒ“ƒeƒVƒmƒX(’˜)C‘O“c‹œ(–ó)CƒVƒ ƒvƒŠƒ“ƒK[ƒtƒFƒAƒ‰[ƒN“Œ‹žC1992”N u‘g‡‚¹ˆÊ‘ŠŠô‰½Šwv uˆÊ‘ŠŠô‰½Šw“ü–åv u‘½ŠpŒ`‚ÌŒ»‘ãŠô‰½Šwv C ¬“‡’è‹g(’˜)C–q–쏑“XC1999”N C ¬“‡’è‹g(’˜)C‹¤—§o”à C1998”N u‚RŽŸŒ³‚ÌŠô‰½Šwv C¬“‡’è‹g(’˜)C’©‘q‘“XC2002”N10ŒŽ C™Œ´Œú‹g(’˜)C’©‘q‘“XC2001”N9ŒŽ C —é–ؐWˆê(’˜)C–Š‘“XC1986”N Œ[–֏‘C“Ç‚Ý•¨•— u‹È–Ê‚Æ‚RŽŸŒ³‘½—l‘Ì‚ðŽ‹‚év C J.ƒEƒB[ƒNƒX(’˜)CŽO‘ºŒìC“ü]°‰h(–ó)CŒ»‘㐔ŠwŽÐC1996”N

51. 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 (in pdf format). http://www.ams.org/notices/199505/sumners.pdf

52. Knot Theory On WWW Home, knot theory on WWW, Links to Personal Pages, Profile. knot theory on WWW. knot theory Group Articles and Preprints; Links to webpages related to knot theory; http://home.hiroshima-u.ac.jp/~teragai/knot-e.html

Home Knot Theory on WWW Links to Personal Pages Profile Knot Theory on WWW Knot (Software for Polynomial Invariants, Braid, Representations, For Linux) @@ WinKnot (Software for Jones polynomial, For Windows) KnotPlot SnapPea ... Journal of Knot Theory and its Ramifications

53. Louis H. Kauffman A topologist working in knot theory discusses the connection between knot theory and statistical mechanics. Sections on cybernetics and knots, Fourier knots and the author's research papers. http://bilbo.math.uic.edu/~kauffman/

Louis H. Kauffman Louis H. Kauffman Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago Chicago, IL 60607-7045 Phone: (312)-996-3066 E-Mail: kauffman@uic.edu Research I am a topologist working in knot theory and its relationships with statistical mechanics, quantum theory, algebra, combinatorics and foundations. This material is based upon work supported by the National Science Foundation under Grant No. DMS - 0245588 and by a grant to study quantum computation and information theory under the auspices of the Defense Advanced Research Projects Agency (DARPA). I am visiting this year (until August 31, 2004) at the University of Waterloo and the Perimeter Institute in Waterloo, Canada. In the winter term I am teaching a course on knots and physics at the university. See Winter Course CO739 for a course description and for notes and problems and downloads for the course. In fall 2003 I also taught a course in knot theory. See the fall course page I recently taught Mathematics 300, a course on writing mathematics. See Write Math!

54. DNA AND KNOT THEORY Open Directory Science Math Topology knot theory Sections on knot tying, mathematical knot theory, knot art, and knot books. History of knot theory - Biographies of early knot theorists. http://www.tiem.utk.edu/~gross/bioed/webmodules/DNAknot.html

DNA AND KNOT THEORY Introduction: DNA is the genetic material of all cells, containing coded information about cellular molecules and processes. DNA consists of two polynucleotide strands twisted around each other in a double helix. The first step in cellular division is to replicate DNA so that copies can be distributed to daughter cells. Additionally, DNA is involved in transcribing proteins that direct cell growth and activities. However, DNA is tightly packed into genes and chromosomes. In order for replication or transcription to take place, DNA must first unpack itself so that it can interact with enzymes. DNA packing can be visualized as two very long strands that have been intertwined millions of times, tied into knots, and subjected to successive coiling. However, replication and transcription are much easier to accomplish if the DNA is neatly arranged rather than tangled up in knots. Enzymes are essential to unpacking DNA. Enzymes act to slice through individual knots and reconnect strands in a more orderly way. Importance: We can gain insight into the unknotting of DNA by using principles of topology. Topologists study the invariant properties of geometric objects, such as knots. Tightly packed DNA in the genes must quickly unknot itself in order for replication or transcription to occur. This is a topological problem.

55. Geometry And The Imagination Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology. http://math.dartmouth.edu/~doyle/docs/gi/gi/gi.html

Bicycle tracks C. Dennis Thron has called attention to the following passage from The Adventure of the Priory School , by Sir Arthur Conan Doyle: `This track, as you perceive, was made by a rider who was going from the direction of the school.' `Or towards it?' `No, no, my dear Watson. The more deeply sunk impression is, of course, the hind wheel, upon which the weight rests. You perceive several places where it has passed across and obliterated the more shallow mark of the front one. It was undoubtedly heading away from the school.' Problems Discuss this passage. Does Holmes know what he's talking about? Try to come up with a method for telling which way a bike has gone by looking at the track it has left. There are all kinds of possibilities here. Which methods do you honestly think will work, and under what conditions? For example, does your method only work if the bike has passed through a patch of wet cement? Would it work for tracks on the beach? Tracks on a patch of dry sidewalk between puddles? Tracks through short, dewy grass? Tracks along a thirty-foot length of brown package-wrapping paper, made by a bike whose tires have been carefully coated with mud, and which has been just ridden long enough before reaching the paper so that the tracks are not appreciably darker at one end of the paper than the other? Try to determine the direction of travel for the idealized bike tracks in Figure Figure 1: Which way did the bicycle go?

56. PlanetMath: Knot Theory knot theory, (Topic). knot theory is the study of knots and links. Much of knot theory is devoted to telling when two knot diagrams represent the same link. http://planetmath.org/encyclopedia/KnotTheory.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List knot theory (Topic) Knot theory is the study of knots and links Roughly a knot is a simple closed curve in , and two knots are considered equivalent if and only if one can be smoothly deformed into another. This will often be used as a working definition as it is simple and appeals to intuition. Unfortunately this definition can not be taken too seriously because it includes many pathological cases, or wild knots, such as the connected sum of an infinite Links are defined in terms of knots, so once we have a definition for knots we have no trouble defining them. Definition A link is a set of disjoint knots. Each knot is a component of the link. In particular a knot is a link of one component. Luckily the knot theorist is not usually interested in the exact form of a knot or link, but rather the in its

57. Search Results Search for papers held at LANL with the word 'knot' in them. http://arXiv.org/find/math/1/fr: knot/0/1/0/past,all/0/1

Search results Back to Search form Next 25 results The URL for this search is http://arXiv.org/find/math/1/fr: knot/0/1/0/past,all/0/1 Showing results 1 through 25 (of 569 total) for knot math.GT/0405547 abs ps pdf other Title: Euclidean tetrahedra and knot invariants Authors: I. G. Korepanov Comments: 8 pages; a shorter version will be published at this http URL Subj-class: Geometric Topology math.RT/0405508 abs ps pdf other Title: Markov traces and knot invariants related to Iwahori-Hecke algebras of type B Authors: Meinolf Geck Sofia Lambropoulou Comments: 27 pages, 6 figures, LaTex document Subj-class: Representation Theory; Geometric Topology MSC-class: Journal-ref: J. fuer die reine und angewandte Mathematik, Vol. 482, pp. 191213 (1997) math.GT/0405504 abs ps pdf other Title: Knot theory related to generalized and cyclotomic Hecke algebras of type B Authors: Sofia Lambropoulou Comments: 35 pages, 8 figures, LaTex document. Title on the abstract page has been corrected; otherwise, v2 is identical to v1 Subj-class: Geometric Topology; Quantum Algebra

58. Knots In Vancouver - Workshop In Knot Theory And 3-Manifolds Home Page. Featured Speakers. Organizing Committee. Registration. Accommodations. Visitors Info. Participants. Programme. Sponsors. Dale Rolfsen s Page. http://www.pims.math.ca/science/2004/KT3Mwksp/

Question, Comments? Contact rolfsen@math.ubc.ca Download Poster (PDF file - 177kb) Pacific Institute for the Mathematical Sciences Last Modified: Wednesday, 03-Mar-2004 14:38:39 PST

59. Jorge Pullin 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

Jorge Pullin Horace Hearne Chair in theoretical Physics, Louisiana State University Adjunct Professor of Physics, University of Utah Adjunct Professor of Physics, PennState Ph.D., Instituto Balseiro Honors and awards Phone/Fax: (225)578-0464 pullin@phys.lsu.edu Horace Hearne Institute for Theoretical Physics Want to hear those pipes? Research. ... Background. Research My research interests cover many aspects of gravitational physics, both classical and quantum mechanical. I am currently focusing on two topics: quantum gravity and black hole collisions . You can also get my complete publication list , but if you want to get the latest, go to the Hearne Institute page and click on publications. The explanations that follow are a bit longish, feel free to skip to the next topic if you get bored! Quantum gravity I collaborate with Rodolfo Gambini, of the University of the Republic in Montevideo, Uruguay, our collaboration has been going on since 1990. We coauthored a book "Loops, knots, gauge theories and quantum gravity" in 1996 and have published many papers together. We study the quantization of general relativity using canonical methods. There is a small community pursuing this kind of research, which is complementary to the mainstream approach to quantum gravity: string theory. String theorists believe that one cannot quantize general relativity because it is not a fundamental theory and one has to replace it with string theory in order to quantize it. General relativity will be an "effective" "low energy" theory.

60. Professor Lomonaco: Knot Theory References knot theory References. Home Page. *** Under Construction ***. Charilaos Aneziris knot theory Primer; Cartoon based on three of Lomonaco s knot theory papers. http://www.cs.umbc.edu/~lomonaco/knot-theory/Knot-Theory.html

Knot Theory References Home Page *** Under Construction *** Charilaos Aneziris' Knot Theory Primer Cartoon based on three of Lomonaco's knot theory papers. A lecture on knots and electrodynamics by Lomonaco Five Dimensional Knot Theory by Lomonaco ( Figures Viewable in HTML) Rob Scharein's Knot Zoo Foxy Knots , and Knot Table Snapshots from the video "Not Knot" The Geometry Center Archives Images The Journal of Knot Theory and Its Ramifications JKTR Knot Theoretic Thought for the day

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