Invariant Definition Table
From Knot Atlas
Jump to navigationJump to search
| Invariant name | KnotInfoTag | KnotTheory | KnotTheorySetter | ReadWiki | Type | WikiPage |
|---|---|---|---|---|---|---|
| Crossings | Crossings | Link Presentation | Crossings | |||
| Knot Number | KnotNumber | Link Presentation | Number | |||
| Knotilus URL | "["<>KnotilusURL[#]<>" "<>NameString[#]<>"'s page]"& | 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 | ||
| Minimal Braid Length | Crossings[BR[#]]& | Knot Presentation | MinimalBraidLength | |||
| Minimal Braid Width | First[BR[#]]& | Knot Presentation | MinimalBraidWidth | |||
| Braid Index | BraidIndex | Knot Presentation | BraidIndex | |||
| Braid Plot | BraidPlot[CollapseBraid[BR[#]], Mode -> "Wiki", Images -> {"BraidPart0.gif", "BraidPart1.gif", "BraidPart2.gif", "BraidPart3.gif", "BraidPart4.gif"}]& | Knot Presentation | BraidPlot | |||
| SymmetryType | SymmetryType | SymmetryType | 3D Invariant | Symmetry_Type | ||
| UnknottingNumber | UnknottingNumber | 3D Invariant | Unknotting_Number | |||
| ThreeGenus | ThreeGenus | 3D Invariant | 3-Genus | |||
| ConcordanceGenus | ConcordanceGenus | 3D Invariant | ConcordanceGenus | |||
| BridgeIndex | BridgeIndex | 3D Invariant | Bridge_Index | |||
| SuperBridgeIndex | SuperBridgeIndex | 3D Invariant | Super_Bridge_Index | |||
| NakanishiIndex | NakanishiIndex | 3D Invariant | Nakanishi_Index | |||
| Jones | Jones[#1][q] & | Jones[#1] = Function[{q}, #2];& | Polynomial Invariant | Jones_Polynomial | ||
| Alexander | Alexander[#1][t] & | Alexander[#1] = Function[{t}, #2];& | Polynomial Invariant | Alexander_Polynomial | ||
| Multivariable Alexander | MultivariableAlexander[#1][t] & | MultivariableAlexander[#1] = Function[{t}, #2];& | Polynomial Invariant | Multivariable_Alexander | ||
| Determinant | KnotDet | Polynomial Invariant | Determinant | |||
| Signature | KnotSignature | Polynomial Invariant | Signature | |||
| Conway | Conway[#1][z] & | Conway[#1] = Function[{z}, #2];& | Polynomial Invariant | Conway_Polynomial | ||
| HOMFLYPT | HOMFLYPT[#1][a, z] & | HOMFLYPT[#1] = Function[{a, z}, #2];& | Polynomial Invariant | HOMFLYPT_Polynomial | ||
| Kauffman | Kauffman[#1][a, z] & | Kauffman[#1] = Function[{a, z}, #2];& | 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 | HyperbolicVolume | HyperbolicVolume[#1]=#2;& | HyperbolicVolume | Hyperbolic Invariant | HyperbolicVolume |
| Conway Notation | conway_notation | Knot Presentation | Conway Notation | |||
| 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 | |||
| Khovanov s-Invariant | khovanov_s_invariant | 4D Invariant | s-Invariant | |||
| Rational Khovanov Polynomial | Kh[#1][q, t] & | Kh[#1] = Function[{q, t}, #2];& | Polynomial Invariant | Rational_Khovanov_Polynomial | ||
| Khovanov Polynomial Table | TabularKh[Kh[#][q, t], KnotSignature[#]+{1,-1}]& | Polynomial Invariant | KhovanovTable | |||
| A-polynomial | A-polynomial |
