| 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 |
| Braid Word |
|
BR[#]& |
|
|
Knot Presentation |
BraidWord |
| 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 |
