Invariant Definition Table: Difference between revisions

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<!-- Invariant name --> <td>Knotilus URL</td>
<!-- Invariant name --> <td>Knotilus URL</td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>KnotilusURL</td>
<!-- KnotTheory = --> <td>"["<>KnotilusURL[#]<>" "<>NameString[#]<>"'s page]"&</td>
<!-- KnotTheorySetter = --> <td></td>
<!-- KnotTheorySetter = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
Line 81: Line 81:
<!-- Type = --> <td>Knot Presentation</td>
<!-- Type = --> <td>Knot Presentation</td>
<!-- WikiPage = --> <td>DT_Code</td>
<!-- WikiPage = --> <td>DT_Code</td>
</tr>
<tr>
<!-- Invariant name --> <td>Braid Word</td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>BR[#]&</td>
<!-- KnotTheorySetter = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Knot Presentation</td>
<!-- WikiPage = --> <td>BraidWord</td>
</tr>
<tr>
<!-- Invariant name --> <td>Minimal Braid Length</td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Crossings[BR[#]]&</td>
<!-- KnotTheorySetter = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Knot Presentation</td>
<!-- WikiPage = --> <td>MinimalBraidLength</td>
</tr>
<tr>
<!-- Invariant name --> <td>Minimal Braid Width</td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>First[BR[#]]&</td>
<!-- KnotTheorySetter = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Knot Presentation</td>
<!-- WikiPage = --> <td>MinimalBraidWidth</td>
</tr>
<tr>
<!-- Invariant name --> <td>Braid Index</td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>BraidIndex</td>
<!-- KnotTheorySetter = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Knot Presentation</td>
<!-- WikiPage = --> <td>BraidIndex</td>
</tr>
<tr>
<!-- Invariant name --> <td>Braid Plot</td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>BraidPlot[CollapseBraid[BR[#]], Mode -> "Wiki", Images -> {"BraidPart0.gif", "BraidPart1.gif", "BraidPart2.gif", "BraidPart3.gif", "BraidPart4.gif"}]&</td>
<!-- KnotTheorySetter = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Knot Presentation</td>
<!-- WikiPage = --> <td>BraidPlot</td>
</tr>
</tr>
<tr>
<tr>
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<!-- KnotInfoTag = --> <td></td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Alexander[#1][t] & </td>
<!-- KnotTheory = --> <td>Alexander[#1][t] & </td>
<!-- KnotTheorySetter = --> <td></td>
<!-- KnotTheorySetter = --> <td>Alexander[#1] = Function[{t}, #2];&</td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<!-- KnotInfoTag = --> <td></td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>MultivariableAlexander[#1][t] & </td>
<!-- KnotTheory = --> <td>MultivariableAlexander[#1][t] & </td>
<!-- KnotTheorySetter = --> <td></td>
<!-- KnotTheorySetter = --> <td>MultivariableAlexander[#1] = Function[{t}, #2];&</td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<!-- KnotInfoTag = --> <td></td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Conway[#1][z] & </td>
<!-- KnotTheory = --> <td>Conway[#1][z] & </td>
<!-- KnotTheorySetter = --> <td></td>
<!-- KnotTheorySetter = --> <td>Conway[#1] = Function[{z}, #2];&</td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<!-- KnotInfoTag = --> <td></td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>HOMFLYPT[#1][a, z] & </td>
<!-- KnotTheory = --> <td>HOMFLYPT[#1][a, z] & </td>
<!-- KnotTheorySetter = --> <td></td>
<!-- KnotTheorySetter = --> <td>HOMFLYPT[#1] = Function[{a, z}, #2];&</td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<!-- KnotInfoTag = --> <td></td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Kauffman[#1][a, z] & </td>
<!-- KnotTheory = --> <td>Kauffman[#1][a, z] & </td>
<!-- KnotTheorySetter = --> <td></td>
<!-- KnotTheorySetter = --> <td>Kauffman[#1] = Function[{a, z}, #2];&</td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<!-- Invariant name --> <td>Hyperbolic Volume</td>
<!-- Invariant name --> <td>Hyperbolic Volume</td>
<!-- KnotInfoTag = --> <td>volume</td>
<!-- KnotInfoTag = --> <td>volume</td>
<!-- KnotTheory = --> <td></td>
<!-- KnotTheory = --> <td>HyperbolicVolume</td>
<!-- KnotTheorySetter = --> <td></td>
<!-- KnotTheorySetter = --> <td>HyperbolicVolume[#1]=#2;&</td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td>HyperbolicVolume</td>
<!-- Type = --> <td>Hyperbolic Invariant</td>
<!-- Type = --> <td>Hyperbolic Invariant</td>
<!-- WikiPage = --> <td>HyperbolicVolume</td>
<!-- WikiPage = --> <td>HyperbolicVolume</td>
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<!-- KnotInfoTag = --> <td></td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Kh[#1][q, t] & </td>
<!-- KnotTheory = --> <td>Kh[#1][q, t] & </td>
<!-- KnotTheorySetter = --> <td></td>
<!-- KnotTheorySetter = --> <td>Kh[#1] = Function[{q, t}, #2];&</td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- WikiPage = --> <td>Rational_Khovanov_Polynomial</td>
<!-- WikiPage = --> <td>Rational_Khovanov_Polynomial</td>
</tr>
<tr>
<!-- Invariant name --> <td>Khovanov Polynomial Table</td>
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>TabularKh[Kh[#][q, t], KnotSignature[#]+{1,-1}]&</td>
<!-- KnotTheorySetter = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- WikiPage = --> <td>KhovanovTable</td>
</tr>
</tr>
<tr>
<tr>

Latest revision as of 15:09, 24 June 2006

Stop hand.png This page is for experts only!
This page stores the definitions of knot invariants understood by ManagingKnotData.m. Please don't edit it without understanding how that program works, and having read Expert Mode Editing.
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
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