21. [hep-th/9905057] Chern-Simons Gauge Theory: Ten Years After A brief review on the progress made in the study of ChernSimons gauge theory since its relation to knot theory was discovered ten years ago is presented. http://arxiv.org/abs/hep-th/9905057

High Energy Physics - Theory, abstract hep-th/9905057 From: Jose M F Labastida [ view email ] Date: Sat, 8 May 1999 09:52:13 GMT (626kb) Chern-Simons Gauge Theory: Ten Years After Authors: J. M. F. Labastida Comments: 62 pages, 21 figures, lecture delivered at the workshop "Trends in Theoretical Physics II", Buenos Aires, November 1998 Subj-class: High Energy Physics - Theory; Geometric Topology Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv hep-th find abs

22. NORTHERN REGIONAL MEETING LMS Northern Regional Meeting and Workshop. University of Liverpool, UK; Meeting 5 June 2002; Workshop 68 June 2002. http://www.lms.ac.uk/meetings/020605_lpool.html

LMS Northern Regional Meeting and Workshop Algebraic Geometry, Knot Theory and Related Topics The University of Liverpool Meeting: Wednesday 5 June 2002 Workshop: 6-8 June 2002 Wednesday Lectures (for a general mathematical audience) 3.00 pm Professor Lou Kauffman (University of Illinois at Chicago) Classifying and applying rational tangles and knots 4.15 pm Tea 4.45 pm What are the simplest algebraic varieties? The meeting will take place on Wednesday afternoon starting at 3 pm and in the evening (6.30 for 7.00) there will be a reception and dinner for speakers and visitors at Staff House in the University of Liverpool. From Thursday 6 to Saturday 8 June there will be an LMS sponsored workshop on Knot Theory and Algebraic Geometry. This will include two 3-lecture courses suitable for postgraduate students: Dr Stavros Garoufalidis (Warwick) The geometry of the Jones polynomial Professor Andrei Tyurin (Steklov Institute, Moscow) Graphs, knots and vector bundles on algebraic curves Other invited speakers for the workshop include L. Chekhov (Steklov Institute), L. Kauffman (University of Illinois), V. Kulikov (Steklov Institute), E. Looijenga (MSRI and Nijmegen), D. Rolfsen (University of British Columbia), M. Scharlemann (University of California). There will be an opportunity for short contributed talks. Some LMS support is available for workshop speakers and U.K. postgraduate students. For further details and to offer a contributed talk or poster contact Professor Peter Giblin (tel: 0151 794 4053/4043, e-mail:

23. The KnotPlot Site data only, no pictures); Knot Diagrams from Dowker Codes; Some excellent references on knot theory. Some favourite figures from my http://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotSquare.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

24. Oporto Meetings On Geometry, Topology And Physics Formerly Meetings on knot theory and Physics held annually in Oporto, Portugal to bring together mathematicians and physicists interested in the interrelation between geometry, topology and physics. http://www.math.ist.utl.pt/~jmourao/om/

Oporto Meetings on Geometry, Topology and Physics Oporto Meetings on Geometry, Topology and Physics (formerly known as the Oporto Meetings on Knot Theory and Physics) take place in Oporto, Portugal, every year. The aim of the Oporto meetings is to bring together mathematicians and physicists interested in the inter-relation between geometry, topology and physics and to provide them with a pleasant and informal environment for scientific interchange. Next Meeting (July 16-19, 2004) XIIth Meeting (July 17-20, 2003) ... Main Page of TQFT Club Free Counter from Counterart

25. Liverpool Knot Theory Group: Knot Programs Four programs, each calculating some invariant from a closed braid presentation. Free to download. Pascal. http://www.liv.ac.uk/~su14/knotprogs.html

Liverpool University Knot Theory Group Programs and Procedures Copies of the following programs and procedures can be downloaded for compilation on your own machine. Some basic descriptions and instructions are attached. Queries can be sent by e-mail to morton@liv.ac.uk This list can be found at URL http://www.liv.ac.uk/~su14/knotprogs.html or by following links from http://www.liv.ac.uk/maths/ See also the list of publications of the Liverpool Knot Theory group , where PostScript copies of some recent preprints can be found. There are at present four programs, each calculating some invariant from a closed braid presentation. In each case the major constraint is the number of braid strings; the growth of calculation time with the number of crossings is roughly quadratic, and so typically it is not difficult to deal with braids having about 100 crossings. Three of the programs are in Pascal. In each case the input required is the braid in terms of standard generators, with no separators, for example 123-2-231. The three programs are br9z.p

26. New Ideas About Knots New ideas about knots This World Wide Web (WWW) site describes a knot theory novice progressing toward an understanding of knot theory and knot manipulation. The topics at this site include http://rdre1.inktomi.com/click?u=http://www.cs.uidaho.edu/~casey931/new_knot/ind

27. WSPC Journals Online Home Journals by Subject Mathematics JKTR Journal of knot theory and Its Ramifications (JKTR). Journal Archive. *PDF Generated from Scanned Images Vol. http://www.worldscinet.com/jktr/mkt/archive.shtml

What's New New Journals Browse Journals Search ... JKTR Journal of Knot Theory and Its Ramifications (JKTR) Journal Archive *PDF Generated from Scanned Images Vol. 13, No. 2 (Mar 2004) Vol. 13, No. 1 (Feb 2004) Vol. 12, No. 8 (Dec 2003) Vol. 12, No. 7 (Nov 2003) Vol. 12, No. 6 (Sep 2003) Vol. 12, No. 5 (Aug 2003)* Vol. 12, No. 4 (Jun 2003) Vol. 12, No. 3 (May 2003)* Vol. 12, No. 2 (Mar 2003)* Vol. 12, No. 1 (Feb 2003)* Vol. 11, No. 8 (Dec 2002)* Vol. 11, No. 7 (Nov 2002)* Vol. 11, No. 6 (Sep 2002)* Vol. 11, No. 5 (Aug 2002)* Vol. 11, No. 4 (Jun 2002)* Vol. 11, No. 3 (May 2002)* Vol. 11, No. 2 (Mar 2002)* Vol. 11, No. 1 (Feb 2002)* Vol. 10, No. 8 (Dec 2001)* Vol. 10, No. 7 (Nov 2001)* Vol. 10, No. 6 (Sep 2001)* Vol. 10, No. 5 (Aug 2001)* Vol. 10, No. 4 (Jun 2001)* Vol. 10, No. 3 (May 2001)* Vol. 10, No. 2 (Mar 2001)* Vol. 10, No. 1 (Feb 2001)* Vol. 9, No. 8 (Dec 2000)* Vol. 9, No. 7 (Nov 2000)* Vol. 9, No. 6 (Sep 2000)* Vol. 9, No. 5 (Aug 2000)* Vol. 9, No. 4 (Jun 2000)* Vol. 9, No. 3 (May 2000)* Vol. 9, No. 2 (Mar 2000)* Vol. 9, No. 1 (Feb 2000)* Vol. 8, No. 8

28. ThinkQuest : Library : Knot Theory knot theory Click to Enter. http://library.thinkquest.org/12295/

Index Math Knot Theory Who knew there was so much to know about mathematical knots? Featuring easy navigation and straightforward menus, this site explores the formulas and factoids associated with the study of topology. While advanced math students will benefit most, the site also includes a glossary and biographies of mathematicians and scientists, handy features for all types of students. Visit Site 1997 ThinkQuest Internet Challenge Languages English Students Jason B. Severn School, Severna Park, MD, United States Stefan Severn School, Severna Park, MD, United States Andrei Severn School, Severna Park, MD, United States Coaches Todd Severn School, Severna Park, MD, United States Todd Severn School, Severna Park, MD, United States Todd Severn School, Severna Park, MD, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

29. David A. Krebes' Personal Home Page Includes a thesis work on knot theory and information on schizophrenia. http://www.telusplanet.net/public/dkrebes

David A. Krebes // text for first two pictures I have devoted much of my life to the study of knots . In my Ph.D. thesis (math), I show that a seamless unknotted loop of rope (circle) cannot be twisted in such a way as to intersect the interior of a sphere in the pair of arcs shown in the first picture (this is commonly known as a square knot). Equivalently: If a curve intersects the interior of a sphere in a square knot then it is genuinely knotted (ie. different from a circle). For example in the second picture the loop (follow it around it is indeed a single loop) is knotted: A long rubber band cannot be manipulated into this shape without breaking it and gluing the ends back together. We call this a "topological" property of the square knot because it is a geometric property that is independent of lengths, angles, or rate of curvature (The size of the circle doesn't matter. In fact even an ellipse or a heart shape would do). The field of "algebraic topology", surely one of the greatest achievements of the twentieth century, expresses many such properties in terms of boundaries . Thus to state the result in yet another way: Take a sphere (it could be egg-shaped) and a transparent, rubbery disc with a thick blue opaque circumference (boundary) and try to manoeuvre it so that the picture inside the sphere (you can't see what the transparent part of the disc is doing) is exactly (in a topological sense) as shown in the first picture, ie. a square knot. You will not succeed. However, even after you have tried many times and gained considerable experience with any of these variations of the problem, you must still organize your experience into a mathematical proof before you can conclude with certainty that you didn't stop just one twist and tug too soon!

30. New Ideas About Knots Recently I ve discovered two books about knot theory that I can read without feeling like I had to learn a foreign language and a foreign alphabet. http://www.cs.uidaho.edu/~casey931/new_knot/

New Ideas about Knots These ideas aren't new to the world, they are new to me (Nancy). They are things that I have discovered since I wrote the basic MegaMath information about knots Recently I've discovered two books about Knot Theory that I can read- without feeling like I had to learn a foreign language and a foreign alphabet. They make me feel perfectly capable of understanding this branch of mathematics. So I have been learning a lot of new things about knot theory. Here are some of my discoveries... Tangled up pictures of tangled up ropes Knot coloring puzzles Knots and counting Pretzel knots

31. Knot Theory References Books and articles about knot theory. The two best books. Livingston, Charles. (1993). knot theory. Washington, DC. Mathematical Association of America. http://www.cs.uidaho.edu/~casey931/new_knot/knbooks.html

Books and articles about Knot Theory The two best books Livingston, Charles. (1993). Knot Theory . Washington, DC.: Mathematical Association of America. ISBN: 0-83385-027-3 Adams, Colin C. (1994). The Knot Book: An Elementary Introduction to the Theory of Knots . New York: W.H. Freeman. ISBN: 0-7167-23929-X

32. Knot Theory Knots whose ends were glued together and their classification form the subject of a branch of Topology known as the knot theory. http://www.cut-the-knot.org/do_you_know/knots.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Knots... Every one knows from experience how to create a knot. We do this all the time, often unwittingly. Knots whose ends were glued together and their classification form the subject of a branch of Topology known as the Knot Theory. On the left there is a picture of the Left Trefoil knot. On the right there is the Right Trefoil knot. It's impossible to continuously (i.e. stretching and twisting but without causing damage to either of them) deform one into another. However, it must be noted that the two knots are topologically equivalent in the sense that there exists a topological transformation that maps one into another. The knots are mirror reflections of each other. In the real world, it can be argued that mirror reflections are only mental images whose existence is entirely different from that of the objects whose reflections they are. In Mathematics, reflections are as real as the objects themselves. Mathematically, reflections are topological transformations that could not be carried out on the real world objects. But

33. ThinkQuest : Library : Knot Theory A brief article on the HOMFLY polynomial and how it is calculated. http://library.thinkquest.org/12295/data/Invariants/Articles/HOMFLY.html

Index Math Knot Theory Who knew there was so much to know about mathematical knots? Featuring easy navigation and straightforward menus, this site explores the formulas and factoids associated with the study of topology. While advanced math students will benefit most, the site also includes a glossary and biographies of mathematicians and scientists, handy features for all types of students. Visit Site 1997 ThinkQuest Internet Challenge Languages English Students Jason B. Severn School, Severna Park, MD, United States Stefan Severn School, Severna Park, MD, United States Andrei Severn School, Severna Park, MD, United States Coaches Todd Severn School, Severna Park, MD, United States Todd Severn School, Severna Park, MD, United States Todd Severn School, Severna Park, MD, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

34. History Of Knot Theory HISTORY OF knot theory. This 2001. EARLY PAPERS ON knot theory. A.Cayley, On a problem of arrangements, Proc. Royal Soc. Edinburgh, Vol. http://www.maths.ed.ac.uk/~aar/knots/

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

35. Knot Theory knot theory. The use audience. One favorite is The Knot Book by Colin Adams. This is listed in a bibilography of knot theory. Now http://grail.cba.csuohio.edu/~somos/knots.html

Knot Theory The use of knots goes back to pre-history, but the mathematical study of knots goes back only to the 19th century. Some of the early investigators were Gauss, Listing, Kirkman, Tait, and Little. Due to connections with applied fields like physics and biology there is increased research today. For examples look at the Titles in Series on Knots and Everything edited by Louis H. Kauffman . There are books which explain the topic for a more popular audience. One favorite is The Knot Book by Colin Adams. This is listed in a bibilography of knot theory . Now I prefer Knots: Mathematics With A Twist by Alexei Sossinsky (translation published 2002) which is more elementary and interesting. The story behind Making a Mathematical Exhbition by Ronald Brown and Tim Porter describes some of the issues involved in presenting knot theory. There are web sites which you can visit to find out more. You can start with the Mega-Math section on knots. Then switch to the KnotPlot site for great color graphics. A less ambitious site is Geometry and the Imagination section on knot notation.

36. A London Mathematical Society Meeting And Workshop London Mathematical Society Meeting and Workshop. University of Liverpool, UK; 58 June 2002. http://www.liv.ac.uk/~pjgiblin/LMSJune02/

London Mathematical Society Meeting and Workshop KNOT THEORY, ALGEBRAIC GEOMETRY AND RELATED TOPICS University of Liverpool, Wednesday 5 June 2002 (LMS Meeting) Thursday 6 - Saturday 8 June 2002 (LMS Workshop) Organising Committee: Hugh Morton, Peter Newstead, Peter Giblin PROGRAMME FOR THE WEDNESDAY LMS MEETING Note that both talks on Wednesday are intended for a general mathematical audience 3.00 LMS Business 3.15 Professor Lou Kauffman (University of Illinois at Chicago): Classifying and applying rational tangles and knots Abstract 4.15 Tea What are the simplest algebraic varieties? Abstract 6.30 for 7 Dinner at Staff House in the University of Liverpool. (The cost for those not being supported by the LMS will be about £18 excluding drinks.) If you wish to attend the Wednesday meeting ONLY... then please send an email to pjgiblin@liv.ac.uk stating whether you wish to attend the dinner in the evening (cost about 18 pounds excluding drinks). See below for travel subsidies for LMS members attending the meeting. PROGRAMME FOR THE 6th-8th JUNE LMS WORKSHOP Changes will be posted from time to time Two 3-lecture courses suitable for postgraduate students: Dr Stavros Garoufalidis (Warwick): The geometry of the Jones ploynomial.

37. The Knot Theory MA3F2 Page The knot theory MA3F2 page. New York W. H. Freeman, 1994. 306p; Livingston, Charles. knot theory Washington, DC Math. Assoc. Amer., 1993. http://www.maths.warwick.ac.uk/~bjs/MA3F2-page.html

The Knot Theory MA3F2 page Course material Prerequisites Little more than linear algebra plus an ability to visualise objects in 3-dimensions. Some knowledge of groups given by generators and relations, and some basic topology would be helpful. The lectures and mind map that follow (from 2003) will be updated as we go through 2004. Mind map Course structure Lectures Writhe and linking numbers, Reidemeister moves and colouring, Colouring, Splittable links and chess boarding, Quadrilateral decomposition, Application of Cramer's rule, The determinant of a link, The colouring group, The number of colourings, Mirrors and codes, The Alexander polynomial, Knot sums, Bridge number and plats, Daisy chains and braids, Braids and Seifert circles, Alexander's theorem: links to braids, Seifert circles and trees, The bracket polynomial, The Jones polynomial, The skein relations, Alternating links, Span(V) = number of crossings, Tangles, Rational tangles and continued fractions, Tangled DNA, Genus and knot sum, Genus of a numerator

38. Prof. W.B.R. Lickorish University of Cambridge. Topology, threedimensional manifolds, knot theory. http://www.dpmms.cam.ac.uk/site2002/People/lickorish_wbr.html

Department of Pure Mathematics and Mathematical Statistics DPMMS People Prof. W.B.R. Lickorish Prof. W.B.R. Lickorish Title: Professor of Geometric Topology College: Pembroke College Room: E1.18 Tel: +44 1223 764283 Research Interests: Topology, three-dimensional manifolds, knot theory Information provided by webmaster@dpmms.cam.ac.uk

39. Liverpool Pure Maths: Knot Theory knot theory Research Group. http://www.liv.ac.uk/~su14/knotgroup.html

Pure Mathematics Knot Theory Dept. Home Page Find someone? Pure home page Knot Theory at Liverpool Members of the Research Group Hugh Morton (e-mail: morton@liv.ac.uk Peter Cromwell (e-mail: spmr02@liv.ac.uk Victor Goryunov (e-mail: goryunov@liv.ac.uk Elisabetta Beltrami (e-mail: elisa@liv.ac.uk Research Students Richard Hadji (e-mail: rhadji@liv.ac.uk Previous Members Anna Aiston Yongju Bae (e-mail: ybae@knu.ac.kr Jonny Hill Sascha Lukac (e-mail: lukac@zib.de Pedro Manchon (e-mail: pmanchon@ma.upm.es Ian Nutt (e-mail: iann@wrox.com Marta Rampichini (e-mail: rampichini@mat.unimi.it Hayley Ryder Paul Strickland (e-mail: p.m.strickland@livjm.ac.uk Publications We maintain a list of our publications , which includes PostScript copies of some recent preprints. There are also some braid programs , mainly in Pascal, for calculating a number of knot invariants. Areas of Interest Hugh's interests include: Fibred knots and links. Braids and closed braid presentations of links.

40. Maple Application Center About Us. Press Room. Careers. Contact Us. knot theory, Cool knots drawn using Maple, © Maplesoft, a division of Waterloo Maple Inc. 2004. Privacy Trademarks. http://www.mapleapps.com/List.asp?CategoryID=14&Category=Knot Theory

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