Invariant Definition Table
From Knot Atlas
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| Invariant name | KnotInfoTag | KnotTheory | ReadWiki | Type | WikiPage |
|---|---|---|---|---|---|
| Crossings | Crossings | Link Presentation | Crossings | ||
| Knot Number | KnotNumber | Link Presentation | Number | ||
| Knotilus URL | KnotilusURL | Navigation | KnotilusURL | ||
| Next Knot | NextKnot | Knot | Navigation | Next_Knot | |
| Previous Knot | PreviousKnot | Knot | Navigation | Previous_Knot | |
| Gauss Code | GaussCode | GaussCode | Link Presentation | Gauss_Code | |
| Planar Diagram | PD | PD | Link Presentation | PD_Presentation | |
| Dowker-Thistlethwaite Code | DTCode | DTCode | Knot Presentation | DT_Code | |
| SymmetryType | SymmetryType | SymmetryType | 3D Invariant | Symmetry_Type | |
| UnknottingNumber | UnknottingNumber | 3D Invariant | Unknotting_Number | ||
| ThreeGenus | ThreeGenus | 3D Invariant | 3-Genus | ||
| BridgeIndex | BridgeIndex | 3D Invariant | Bridge_Index | ||
| SuperBridgeIndex | SuperBridgeIndex | 3D Invariant | Super_Bridge_Index | ||
| NakanishiIndex | NakanishiIndex | 3D Invariant | Nakanishi_Index | ||
| Jones | Jones[#1][q] & | Polynomial Invariant | Jones_Polynomial | ||
| Alexander | Alexander[#1][t] & | Polynomial Invariant | Alexander_Polynomial | ||
| Determinant | KnotDet | Polynomial Invariant | Determinant | ||
| Signature | KnotSignature | Polynomial Invariant | Signature | ||
| Conway | Conway[#1][z] & | Polynomial Invariant | Conway_Polynomial | ||
| HOMFLYPT | HOMFLYPT[#1][a, z] & | Polynomial Invariant | HOMFLYPT_Polynomial | ||
| Kauffman | Kauffman[#1][a, z] & | Polynomial Invariant | Kauffman_Polynomial | ||
| Khovanov-Rozansky Polynomial | Polynomial Invariant | Khovanov_Rozansky_Polynomial | |||
| Vassiliev2 | Vassiliev[2] | Vassiliev Invariant | V_2 | ||
| Vassiliev3 | Vassiliev[3] | Vassiliev Invariant | V_3 | ||
| Smooth 4-Genus | smooth_4_genus | 4D Invariant | Smooth4Genus | ||
| Topological 4-Genus | topological_4_genus | 4D Invariant | Topological4Genus | ||
| Thurston-Bennequin Number | thurston_bennequin_number | 3D Invariant | ThurstonBennequinNumber | ||
| Hyperbolic Volume | volume | Hyperbolic Invariant | HyperbolicVolume | ||
| Conway Notation | conway_notation | Knot Presentation | ConwayNotation | ||
| Concordance Order | concordance_order | Concordance Invariant | ConcordanceOrder | ||
| Algebraic Concordance Order | concordance_order_algebraic | Concordance Invariant | AlgebraicConcordanceOrder | ||
| Ozsvath-Szabo Tau Invariant | ozsvath_szabo_tau | 4D Invariant | TauInvariant | ||
| Rational Khovanov Homology | Kh[#1][q, t] & | Polynomial Invariant | Rational_Khovanov_Polynomial |
