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| About site: http://www.maths.warwick.ac.uk/~bjs/MA3F2-page.html |
Title: Math/Topology/Knot Theory - A Third Year Lecture Course on Knots Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.
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The Knot Theory MA3F2 pageThe Knot Theory MA3F2 page Course material Prerequisites Little more than linear algebraplus an ability to visualise objects in 3-dimensions. Some knowledge ofgroups given by generators and relations, and some basic topology wouldbe helpful. The lectures and mind map that follow (from 2006) will beupdated as we go through 2007. Mind map Course structure. Lectures 1 Writheand linking numbers, 2 Reidemeister moves and colouring, 3 Colouring, 4 Splittable links and chess boarding, 5 Quadrilateral decomposition, 6 Application of Cramer's rule, 7 The determinant of a link, 8 The colouring group, 9 The number of colourings, 10 Mirrors and codes, 11 The Alexander polynomial, 12 Knot sums, 13Bridge number and plats, 14 Daisychains and braids, 15 Braids and Seifertcircles, 16 Alexander's theorem: links tobraids, 17 Seifert circles and trees, 18 The bracket polynomial, 19 The Jones polynomial, 20 The skein relations, 21 Alternating links, 22 Span(V) = number of crossings, 23 Tangles, 24Rational tangles and continued fractions, 25Tangled DNA, 26 Genus and knot sum, 27 Genus of a numerator, 28 Conway polynomial, 29 Conway, Alexander, Jones and HOMFLY, 30 Not Knot video, Examples 1, 2, 3, 4, 5, 6, 7, 8, Solutions 1, 2, 3, 4, 5, 6, 7 , 8, 9, 10, 11, 12 Plan your degree course entry Recommended for the course: Adams, C. C. The Knot Book: An ElementaryIntroduction to the Mathematical Theory of Knots. NewYork: W. H. Freeman, 1994. 306p Livingston, Charles. KnotTheory Washington, DC: Math. Assoc. Amer., 1993. 240 p. Cromwell, Peter Knots and Links Cambridge University Press, 2004. 346 p. Last updated 2/1/2007. Reload for latest update. Download the entiresite hereLinks used in notes The Rolfsen knot table. Can you see the isotopy between thePerko pair? An unknotting of a `Gordian knot'. Pictures of knots with 10crossings taken from the tables of Tate and Little. The Perko pairis 5II and 6VI. Here 6VI is omitted. Where crossings are not indicatedassume alternating (over, under, over, under ...). 8_17 is achiral 8_17 with Seifert circles Jones polynomials of knots up to10crossings together with their Dowker-Thistlethwaite codes. Pictures of rational knots31 through 81 with their Conway notation and another view of 31 to 77. From plats to bridges. Simplifying a 4-plat. From knot to braid. A table of braid representationsof knots. A list of Alexander and Jones polynomials. Finding the maximal degree term inthebracket polynomial. A Maple worksheet for calculatingAlexanderpolynomials and determinants of knots and links. A DOS program to calculate knotpolynomials. A java program to calculate the Jonespolynomial. Knotted DNA and a DNA page from the KnotsExhibition at Bangor The trefoil knot bounds atorus with a hole. An aid to understanding rational/2-bridgeknot construction and notation. Visual aids for the Not Knot video. Knots from the Alambra and elsewhere. Celtic knots, and a quote from Tait. Exams The 1997 exam. The 1998 exam. The 1998 exam solutions. The 1999 exam. The 1999 exam solutions. The 2000 exam. The 2000 exam solutions. The 2001 exam. The 2001 exam solutions. The 2002 exam. The 2002 exam solutions. The 2003 exam. The 2003 exam solutions. The 2004 exam. The 2004 exam solutions. The 2005 exam. The 2005 exam solutions. The 2006 exam. The 2006 exam solutions. The 1997/98 Syllabus The 1998/99/00 Syllabus  Please email me if you have anycomments, questions, criticisms or need for clarification regardinglectures or web pages.Home again |
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Includes | examples, | solutions, | knot | tables, | pretty | pictures. | | Course | material | includes: | colouring, | Alexander | and | Jones | polynomials, | tangles | and | braids. |
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http://www.maths.warwick.ac.uk/~bjs/MA3F2-page.html
A Third Year Lecture Course on Knots 2008 December
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Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.
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