Knot polynomial
This opened up avenues of research linking knot theory and statistical mechanics.Edward Witten demonstrated that the Jones polynomial, and similar Jones-type invariants, had an interpretation in Chern–Simons theory.Viktor Vasilyev and Mikhail Goussarov started the theory of finite type invariants of knots.The coefficients of the previously named polynomials are known to be of finite type (after perhaps a suitable "change of variables").The graded Euler characteristic of the knot Floer homology of Peter Ozsváth and Zoltan Szabó is the Alexander polynomial.
skein relationsmathematicalknot theoryknot invariantpolynomialAlexander polynomialJames Waddell Alexander IIJohn Conwayskein relationAlexander–Conway polynomialVaughan JonesJones polynomialHOMFLY polynomialLouis Kauffmanpartition functionbracket polynomialframed knotsstatistical mechanicsEdward WittenChern–Simons theoryViktor VasilyevMikhail Goussarovfinite type invariantsFloer homologyEuler characteristicknot Floer homologyPeter OzsváthZoltan SzabóAlexander–Briggs notationUnknotTrefoil KnotFigure-eight KnotCinquefoil KnotGranny KnotSquare KnotAlexander polynomialsKauffman polynomialGraph polynomialTutte polynomialLickorish, W. B. R.Graduate Texts in MathematicsHyperbolicFigure-eightThree-twistStevedoreEndlessCarrick matPerko pairConway knotKinoshita–Terasaka knot(−2,3,7) pretzelWhiteheadBorromean ringsL10a140SatelliteComposite knotsGrannySquareKnot sumTrefoilCinquefoilSeptafoilUnlinkSolomon'sInvariantsAlternatingArf invariantBridge no.2-bridgeBrunnianChiralityInvertibleCrosscap no.Crossing no.Finite type invariantHyperbolic volumeKhovanov homologyKnot groupLink groupLinking no.AlexanderBracketHOMFLYKauffmanPretzelStick no.TricolorabilityUnknotting no.problemoperationsConway notationDowker–Thistlethwaite notationMutationReidemeister moveTabulationAlexander's theoremBraid theoryConway sphereComplementDouble torusFiberedList of knots and linksRibbonTait conjecturesWritheSurgery theory