{"id":64,"date":"2022-11-04T22:40:49","date_gmt":"2022-11-04T21:40:49","guid":{"rendered":"https:\/\/project.inria.fr\/topal\/?page_id=64"},"modified":"2023-01-17T21:19:34","modified_gmt":"2023-01-17T20:19:34","slug":"knots-3-manifolds","status":"publish","type":"page","link":"https:\/\/project.inria.fr\/topal\/knots-3-manifolds\/","title":{"rendered":"Knots & 3-manifolds"},"content":{"rendered":"

We refer to the Acknowledgment<\/a> page for contributors and methodology of computation.<\/p>\n

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Prime knots of up to 19 crossings:<\/h1>\n

The following folders contain the first prime knots of up to 19 crossings, with basic information:<\/p>\n

    \n
  1. knot names [name<\/strong>] and signatures [knot_sig<\/strong>],<\/li>\n
  2. alternating\/non-alternating [alternating<\/strong>], torus\/non-torus [torus<\/strong>], satellite\/non-satellite [satellite<\/strong>], hyperbolic\/non-hyperbolic [hyperbolic<\/strong>], with value in 0\/1<\/strong>,<\/li>\n<\/ol>\n

    Notice<\/strong><\/p>The knots diagrams have been taken from the Regina website<\/a> where more information and representations of knot diagrams are available (DT code, DT name, topological structure). We use the same names for the knot diagrams. The knot census has been constituted thanks to the effort of many mathematicians and computer scientist: see Acknowledgment.<\/a><\/p>\n

    Files have been divided to contain at most 10,000,000 knots.<\/div>\n\n\n\n\n\n\n\n\n\n\n\n
    Knots from 3 to 17 crossings<\/a><\/td>\nKnots of 19 crossings #4<\/a><\/td>\nKnots of 19 crossings #13<\/a><\/td>\nKnots of 19 crossings #22<\/a><\/td>\n<\/tr>\n
    Knots of 18 crossings #1<\/a><\/td>\nKnots of 19 crossings #5<\/a><\/td>\nKnots of 19 crossings #14<\/a><\/td>\nKnots of 19 crossings #23<\/a><\/td>\n<\/tr>\n
    Knots of 18 crossings #2<\/a><\/td>\nKnots of 19 crossings #6<\/a><\/td>\nKnots of 19 crossings #15<\/a><\/td>\nKnots of 19 crossings #24<\/a><\/td>\n<\/tr>\n
    Knots of 18 crossings #3<\/a><\/td>\nKnots of 19 crossings #7<\/a><\/td>\nKnots of 19 crossings #16<\/a><\/td>\nKnots of 19 crossings #25<\/a><\/td>\n<\/tr>\n
    Knots of 18 crossings #4<\/a><\/td>\nKnots of 19 crossings #8<\/a><\/td>\nKnots of 19 crossings #17<\/a><\/td>\nKnots of 19 crossings #26<\/a><\/td>\n<\/tr>\n
    Knots of 18 crossings #5<\/a><\/td>\nKnots of 19 crossings #9<\/a><\/td>\nKnots of 19 crossings #18<\/a><\/td>\nKnots of 19 crossings #27<\/a><\/td>\n<\/tr>\n
    Knots of 19 crossings #1<\/a><\/td>\nKnots of 19 crossings #10<\/a><\/td>\nKnots of 19 crossings #19<\/a><\/td>\nKnots of 19 crossings #28<\/a><\/td>\n<\/tr>\n
    Knots of 19 crossings #2<\/a><\/td>\nKnots of 19 crossings #11<\/a><\/td>\nKnots of 19 crossings #20<\/a><\/td>\nKnots of 19 crossings #29<\/a><\/td>\n<\/tr>\n
    Knots of 19 crossings #3<\/a><\/td>\nKnots of 19 crossings #12<\/a><\/td>\nKnots of 19 crossings #21<\/a><\/td>\nKnots of 19 crossings #30<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Jones polynomials of knots:<\/h3>\n

    The following folders contain the Jones polynomials of the first prime knots with up to 19 crossings, with:<\/p>\n

      \n
    1. knot names [name<\/strong>],<\/li>\n
    2. Jones polynomial [jones_poly<\/strong>], encoded as a sparse list of monomials “i a<\/strong> j b …” <\/strong>standing for “a X^i + b X^j …”<\/strong><\/li>\n<\/ol>\n

      Notice<\/strong><\/p> The Jones polynomials follow the convention of “Bar Nathan – On Khovanov’s categorification of the Jones polynomial<\/a>“<\/em> <\/div>\n

      \u00a0<\/em><\/p>\n\n\n\n\n\n\n\n\n\n\n\n
      Knots from 3 to 17 crossings<\/a><\/td>\nKnots of 19 crossings #4<\/a><\/td>\nKnots of 19 crossings #13<\/a><\/td>\nKnots of 19 crossings #22<\/a><\/td>\n<\/tr>\n
      Knots of 18 crossings #1<\/a><\/td>\nKnots of 19 crossings #5<\/a><\/td>\nKnots of 19 crossings #14<\/a><\/td>\nKnots of 19 crossings #23<\/a><\/td>\n<\/tr>\n
      Knots of 18 crossings #2<\/a><\/td>\nKnots of 19 crossings #6<\/a><\/td>\nKnots of 19 crossings #15<\/a><\/td>\nKnots of 19 crossings #24<\/a><\/td>\n<\/tr>\n
      Knots of 18 crossings #3<\/a><\/td>\nKnots of 19 crossings #7<\/a><\/td>\nKnots of 19 crossings #16<\/a><\/td>\nKnots of 19 crossings #25<\/a><\/td>\n<\/tr>\n
      Knots of 18 crossings #4<\/a><\/td>\nKnots of 19 crossings #8<\/a><\/td>\nKnots of 19 crossings #17<\/a><\/td>\nKnots of 19 crossings #26<\/a><\/td>\n<\/tr>\n
      Knots of 18 crossings #5<\/a><\/td>\nKnots of 19 crossings #9<\/a><\/td>\nKnots of 19 crossings #18<\/a><\/td>\nKnots of 19 crossings #27<\/a><\/td>\n<\/tr>\n
      Knots of 19 crossings #1<\/a><\/td>\nKnots of 19 crossings #10<\/a><\/td>\nKnots of 19 crossings #19<\/a><\/td>\nKnots of 19 crossings #28<\/a><\/td>\n<\/tr>\n
      Knots of 19 crossings #2<\/a><\/td>\nKnots of 19 crossings #11<\/a><\/td>\nKnots of 19 crossings #20<\/a><\/td>\nKnots of 19 crossings #29<\/a><\/td>\n<\/tr>\n
      Knots of 19 crossings #3<\/a><\/td>\nKnots of 19 crossings #12<\/a><\/td>\nKnots of 19 crossings #21<\/a><\/td>\nKnots of 19 crossings #30<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      HOMFLY-PT polynomials of knots:<\/h3>\n

      The following folders contain the HOMFLY-PT polynomials of the first prime knots with up to 19 crossings, with:<\/p>\n

        \n
      1. knot names [name<\/strong>],<\/li>\n
      2. HOMFLY-PT polynomial [homfly_poly<\/strong>], encoded as a sparse list of monomials “i j a<\/strong> k l b …” <\/strong>standing for “a L^i M^j + b L^k M^l …”<\/strong><\/li>\n<\/ol>\n

        Notice<\/strong><\/p>The HOMFLY-PT polynomials are given with variables L and M.<\/div>\n\n\n\n\n\n\n\n\n\n\n\n
        Knots from 3 to 17 crossings<\/a><\/td>\nKnots of 19 crossings #4<\/a><\/td>\nKnots of 19 crossings #13<\/a><\/td>\nKnots of 19 crossings #22<\/a><\/td>\n<\/tr>\n
        Knots of 18 crossings #1<\/a><\/td>\nKnots of 19 crossings #5<\/a><\/td>\nKnots of 19 crossings #14<\/a><\/td>\nKnots of 19 crossings #23<\/a><\/td>\n<\/tr>\n
        Knots of 18 crossings #2<\/a><\/td>\nKnots of 19 crossings #6<\/a><\/td>\nKnots of 19 crossings #15<\/a><\/td>\nKnots of 19 crossings #24<\/a><\/td>\n<\/tr>\n
        Knots of 18 crossings #3<\/a><\/td>\nKnots of 19 crossings #7<\/a><\/td>\nKnots of 19 crossings #16<\/a><\/td>\nKnots of 19 crossings #25<\/a><\/td>\n<\/tr>\n
        Knots of 18 crossings #4<\/a><\/td>\nKnots of 19 crossings #8<\/a><\/td>\nKnots of 19 crossings #17<\/a><\/td>\nKnots of 19 crossings #26<\/a><\/td>\n<\/tr>\n
        Knots of 18 crossings #5<\/a><\/td>\nKnots of 19 crossings #9<\/a><\/td>\nKnots of 19 crossings #18<\/a><\/td>\nKnots of 19 crossings #27<\/a><\/td>\n<\/tr>\n
        Knots of 19 crossings #1<\/a><\/td>\nKnots of 19 crossings #10<\/a><\/td>\nKnots of 19 crossings #19<\/a><\/td>\nKnots of 19 crossings #28<\/a><\/td>\n<\/tr>\n
        Knots of 19 crossings #2<\/a><\/td>\nKnots of 19 crossings #11<\/a><\/td>\nKnots of 19 crossings #20<\/a><\/td>\nKnots of 19 crossings #29<\/a><\/td>\n<\/tr>\n
        Knots of 19 crossings #3<\/a><\/td>\nKnots of 19 crossings #12<\/a><\/td>\nKnots of 19 crossings #21<\/a><\/td>\nKnots of 19 crossings #30<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        Hyperbolic volumes of hyperbolic knots<\/h3>\n

        The following files contains the hyperbolic volumes of hyperbolic knots (separated into alternating and non-alternating):<\/p>\n