KnotInfo: Table of Knots

Use the advanced features to specify the knots you want tabulated. Then select invariants and properties from the sections below. Click SUBMIT anywhere to produce your desired table.

 Either select knots you want tabulated by selecting specific search criteria:
 (select invariant)\nAlexander Polynomial\nAlgebraic Concordance Order\nAlgebraic Unknotting Number\nAlternating\nArc Index\nArf Invariant\nBraid Index\nBraid Length\nBridge Index\nChern-Simons Invariant\nCrosscap Number\nCrossing Number\nDeterminant\nDouble Slice Genus\nEpsilon\nFibered\nFull Symmetry Group\nL-space Knot\nLongitude Length\nLongitude Translation\nMaximum Cusp Volume\nMeridian Length\nMeridian Translation\nMorse-Novikov Number\nNakanishi Index\nName Rank\nNu\nOther Short Geodesics\nOzsvath-Szabo Tau-Invariant\nPolygon Index\nPositive\nPositive Braid\nQuasipositive\nRasmussen Invariant\nRopelength\nSignature\nSmooth 4D Crosscap Number\nSmooth Concordance Genus\nSmooth Concordance Order\nSmooth Four Genus\nStrongly Quasipositive\nSuper Bridge Index\nSymmetry Type\nThree Genus\nThurston-Bennequin Number\nTopological 4D Crosscap Number\nTopological Concordance Genus\nTopological Concordance Order\nTopological Four Genus\nTunnel Number\nTuraev Genus\nUnknotting Number\nVolume\nWidth\n =\n<\n>\n≠\n and\nor\n (select invariant)\nAlexander Polynomial\nAlgebraic Concordance Order\nAlgebraic Unknotting Number\nAlternating\nArc Index\nArf Invariant\nBraid Index\nBraid Length\nBridge Index\nChern-Simons Invariant\nCrosscap Number\nCrossing Number\nDeterminant\nDouble Slice Genus\nEpsilon\nFibered\nFull Symmetry Group\nL-space Knot\nLongitude Length\nLongitude Translation\nMaximum Cusp Volume\nMeridian Length\nMeridian Translation\nMorse-Novikov Number\nNakanishi Index\nName Rank\nNu\nOther Short Geodesics\nOzsvath-Szabo Tau-Invariant\nPolygon Index\nPositive\nPositive Braid\nQuasipositive\nRasmussen Invariant\nRopelength\nSignature\nSmooth 4D Crosscap Number\nSmooth Concordance Genus\nSmooth Concordance Order\nSmooth Four Genus\nStrongly Quasipositive\nSuper Bridge Index\nSymmetry Type\nThree Genus\nThurston-Bennequin Number\nTopological 4D Crosscap Number\nTopological Concordance Genus\nTopological Concordance Order\nTopological Four Genus\nTunnel Number\nTuraev Genus\nUnknotting Number\nVolume\nWidth\n =\n<\n>\n≠\n and\nor\n (select invariant)\nAlexander Polynomial\nAlgebraic Concordance Order\nAlgebraic Unknotting Number\nAlternating\nArc Index\nArf Invariant\nBraid Index\nBraid Length\nBridge Index\nChern-Simons Invariant\nCrosscap Number\nCrossing Number\nDeterminant\nDouble Slice Genus\nEpsilon\nFibered\nFull Symmetry Group\nL-space Knot\nLongitude Length\nLongitude Translation\nMaximum Cusp Volume\nMeridian Length\nMeridian Translation\nMorse-Novikov Number\nNakanishi Index\nName Rank\nNu\nOther Short Geodesics\nOzsvath-Szabo Tau-Invariant\nPolygon Index\nPositive\nPositive Braid\nQuasipositive\nRasmussen Invariant\nRopelength\nSignature\nSmooth 4D Crosscap Number\nSmooth Concordance Genus\nSmooth Concordance Order\nSmooth Four Genus\nStrongly Quasipositive\nSuper Bridge Index\nSymmetry Type\nThree Genus\nThurston-Bennequin Number\nTopological 4D Crosscap Number\nTopological Concordance Genus\nTopological Concordance Order\nTopological Four Genus\nTunnel Number\nTuraev Genus\nUnknotting Number\nVolume\nWidth\n =\n<\n>\n≠\n and\nor\n (select invariant)\nAlexander Polynomial\nAlgebraic Concordance Order\nAlgebraic Unknotting Number\nAlternating\nArc Index\nArf Invariant\nBraid Index\nBraid Length\nBridge Index\nChern-Simons Invariant\nCrosscap Number\nCrossing Number\nDeterminant\nDouble Slice Genus\nEpsilon\nFibered\nFull Symmetry Group\nL-space Knot\nLongitude Length\nLongitude Translation\nMaximum Cusp Volume\nMeridian Length\nMeridian Translation\nMorse-Novikov Number\nNakanishi Index\nName Rank\nNu\nOther Short Geodesics\nOzsvath-Szabo Tau-Invariant\nPolygon Index\nPositive\nPositive Braid\nQuasipositive\nRasmussen Invariant\nRopelength\nSignature\nSmooth 4D Crosscap Number\nSmooth Concordance Genus\nSmooth Concordance Order\nSmooth Four Genus\nStrongly Quasipositive\nSuper Bridge Index\nSymmetry Type\nThree Genus\nThurston-Bennequin Number\nTopological 4D Crosscap Number\nTopological Concordance Genus\nTopological Concordance Order\nTopological Four Genus\nTunnel Number\nTuraev Genus\nUnknotting Number\nVolume\nWidth\n =\n<\n>\n≠\n and\nor\n (select invariant)\nAlexander Polynomial\nAlgebraic Concordance Order\nAlgebraic Unknotting Number\nAlternating\nArc Index\nArf Invariant\nBraid Index\nBraid Length\nBridge Index\nChern-Simons Invariant\nCrosscap Number\nCrossing Number\nDeterminant\nDouble Slice Genus\nEpsilon\nFibered\nFull Symmetry Group\nL-space Knot\nLongitude Length\nLongitude Translation\nMaximum Cusp Volume\nMeridian Length\nMeridian Translation\nMorse-Novikov Number\nNakanishi Index\nName Rank\nNu\nOther Short Geodesics\nOzsvath-Szabo Tau-Invariant\nPolygon Index\nPositive\nPositive Braid\nQuasipositive\nRasmussen Invariant\nRopelength\nSignature\nSmooth 4D Crosscap Number\nSmooth Concordance Genus\nSmooth Concordance Order\nSmooth Four Genus\nStrongly Quasipositive\nSuper Bridge Index\nSymmetry Type\nThree Genus\nThurston-Bennequin Number\nTopological 4D Crosscap Number\nTopological Concordance Genus\nTopological Concordance Order\nTopological Four Genus\nTunnel Number\nTuraev Genus\nUnknotting Number\nVolume\nWidth\n =\n<\n>\n≠\n and\nor\n

 Or specify search criterion with text input:

e.g.: (signature=0 and rasmussen_invariant != 0) or alexander_polynomial='1' [Search Help]

The result includes knots with unknown values of the invariants used in the search criterion (including those with range values).

 3D Presentations and Properties Adequate Braid Notation Pretzel Notation Small or Large Almost Alternating Fibered Quasialternating Symmetry Type Alternating Monodromy Seifert Matrix Two-Bridge Notation Boundary Slopes Montesinos Notation
 Positivity and Strong Quasipositivity Positive Braid Positive SQ-Positive Q-Positive Pos. Braid Notation Pos. PD Notation SQ-Postive Braid Q-Positive Braid
 4D Numeric Invariants smooth unless indicated algebraic (Alg.) or topologial (Top.) Arf Invariant Concordance Order Concordance Genus (Top.) Genus-4D (Top.) Clasp Number-4D Concordance Order (Alg.) Double Slice Genus Signature Crosscap Number-4D Concordance Order (Top.) Genus-4D Signature function Crosscap Number-4D (Top.) Concordance Genus
 Polynomial Invariants Alexander Conway Jones Kauffman A-Polynomial HOMFLY
 Vectorized Polynomial Invariants (click to view) Alexander (vector) Conway (vector) Jones (vector) Kauffman (vector) A-Polynomial HOMFLY (vector)
 Knot Homology Properties and Numeric Invariants Epsilon Nu Ozsvath-Szabo tau Rasmussen s L-space
 Knot Homology Polynomial Invariants KH Unred Z Poly KH Red Z Poly KH Red Q Poly KH Red Mod2 Poly KH Odd Red Z Poly KH Odd Red Q Poly KH Odd Red Mod2 Poly HFK Polyomial
 Vectorized Knot Homology Polynomial Invariants (click to view) KH Unred Z Vector KH Red Z Vector KH Red Q Vector KH Red Mod2 Vector KH Odd Red Z Vector KH Odd Red Q Vector KH Odd Red Mod2 Vector HFK Polyomial Vector

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