AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |
Back to Blog
Justin roberts knots knotes1/16/2024 ![]() ![]() Here you can find code to create a Mandlebrot set. Here you can find Manual Zoom on the Mandlebrot set. Here you can find Zoom video of Mandlbrot set on Youtube link. Here you can find chaos game applet for Sierpinski gasket fractals. Here you can find Sierpinski Triangle images including zoom. Here is a link to a Maple worksheet on taking integrals.Īnd the course schedule (permissions required). Here is a Maple worksheet to use as a template for graphing functions. Here is a link to the a Maple worksheet on Newton's Method. Here is a link to the a Maple worksheet on Reimann Sums (useful in 111 and 112). Here is a link to the a very basic introduction to Maple. Introduction to knot theory, by R.Crowell and R.Fox īraids, links and mapping class groups, by Joan Birman.Math 121: Section A: Tues and Thurs 8:00-9:15am, Section B: Tues and Thurs 9:30-10:45am, Section C: Tues and Thurs 12:30-1:45pmĬontains many resources for the class (login required).Ĭontains many resources for the class including the syllabusĪnd the course schedule (permission required). The Software Archive, a site for people doing computational stuff with low-dimensional topology. ![]() ![]() Table of Knot Invariants, by Charles Livingston Knot theory and the Alexander polynomial, by Reagin McNeill.īy Dror Bar-Natan and Scott Morrison. Topological invariants of knots: three routes to the Alexander polynomial, by Edward Long. Introduction to knots and a survey of knot colorings.ģ-coloring and other elementary invariants of knots, by Jozef Przytycki. The Trieste look at knot theory, by Jozef Przytycki. An advanced gauge theory approach.Īn introduction to knot Floer homology, by Ciprian Manolescu. Two Lectures On The Jones Polynomial And Khovanov Homology, by Edward Witten. Jeff Weeks, Computation of hyperbolic structures in knot theory Lee Rudolph, Knot theory of complex plane curvesġ1. Charles Livingston, A survey of classical knot concordanceĩ. Louis Kauffman, Diagrammatic methods for invariants of knots andħ. Jim Hoste, The enumeration and classiffication of knots and linksĦ. John Etnyre, Legendrian and transversal knotsĥ. Birman and Tara Brendle, Braids and knotsģ. Other resources Handbook of Knot Theory (W.Menasco and M.Thistlethwaite, editors)Ģ. Purcell: Notes on hyperbolic knot theory by Jessica S. Prasolov-Sossinsky: Knots, links, braids and 3-manifolds by V.V.Prasolov and A.B.Sossinsky Lickorish: An introduction to knot theory by W.B.Raymond Lickorish. Reading: P.Turner, "Five lectures on Khovanov homology."Ĭromwell: Knots and links by Peter Cromwell Reading: H.Murakami "An introduction to the Volume Conjecture", A.Schmitgen thesis.Īpproaches to Khovanov homology: Khovanov, Viro, Bar-Natan, spanning tree model, Turaev genus and homological width. Proof for figure-8 knot, support for the Volume Conjecture. Reading: Purcell ch 9, Ratcliffe Foundations of hyperbolic manifolds chapter 10, Milnor, Lackenby-Agol-DThurston. Hyperbolic volume, properties, diagrammatic bounds. Hyperbolic geometry of 3-manifolds, figure-8 knot complement, ideal tetrahedra, gluing and completeness equations. Reading: slope conj (Garoufalidis), adequate knots (FKP) and survey (FKP), Montesinos boundary slopes (Dunfield), boundary slopes (Culler-Shalen), slope conj for links (R.v.Veen), strong slope conj (Kalfagianni-Tran) Reading: Lickorish ch 13-14, Prasolov-Sossinsky ch 8, Masbaum-Vogelīoundary slopes, Slope Conjecture(s), proof for adequate knots. H.Murakami, "An introduction to the Volume Conjecture".Ĭalculations with Jones-Wenzl idempotents, colored Jones polynomial. Reading: Chmutov, Duzhin, Mostovoy Vassiliev Knot Invariants ch 2.6 and appendix. Representations, R-matrices and Yang-Baxter equation, colored Jones polynomial, cabling formula. Reading: Bollobas Modern Graph Theory ch X, Jones 1, Jones 2, Watson, Rolfsen. Tait graph and spanning-tree expansion for the Jones polynomial. Reading: Lickorish ch 3,5, Prasolov-Sossinsky ch 2.3, Cromwell ch 9. Alternating knots and proof of Tait's conjecture. Reading: Lickorish ch 6,7,11, Cromwell ch 7, Rolfsen ch 6-8, Murasugi ch 6. Wirtinger presentation for the knot group. Many approaches to Alexander polynomial: Seifert matrices, homology of infinite cyclic cover, Fox calculus, Conway polynomial. Reading: Lickorish ch 2,8, Cromwell ch 5-6, Murasugi ch 5, 6.4. Seifert surfaces, circuits and genus, Yamada's theorem and Vogel's algorithm. Reading: Prasolov-Sossinsky ch 3, Cromwell ch 8, 10.1, 10.4, Rolfsen braids. Rational tangles, rational links, 2-bridge links, plats. Reading: Lickorish ch 1, Cromwell ch 1-4, Prasolov-Sossinsky ch 1, Knotes ch 1-2, Lackenby survey.īraid group, Alexander and Markov theorems, braid index. The Graduate Center, City University of New York (CUNY) MATH 82800: Knot Theory ĭefinitions, diagrams, Reidemeister moves, wild knots, connect sum, unknotting, satellite knots, historical overview of knot theory. ![]()
0 Comments
Read More
Leave a Reply. |