Invariant Definition Table: Difference between revisions

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<tr>
<tr>
<th>Invariant name</th>
<th>Invariant name</th>
⚫
<th>KnotInfoTag</th>
<th>KnotTheory</th>
<th>KnotTheory</th>
⚫
<th>LivingstonTag</th>
<th>ReadLivingston</th>
<th>ReadWiki</th>
<th>ReadWiki</th>
<th>Type</th>
<th>Type</th>
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<tr>
<tr>
<!-- Invariant name --> <td>Crossings</td>
<!-- Invariant name --> <td>Crossings</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Crossings</td>
<!-- KnotTheory = --> <td>Crossings</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Link Presentation</td>
<!-- Type = --> <td>Link Presentation</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Knot Number</td>
<!-- Invariant name --> <td>Knot Number</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>KnotNumber</td>
<!-- KnotTheory = --> <td>KnotNumber</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Link Presentation</td>
<!-- Type = --> <td>Link Presentation</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Knotilus URL</td>
<!-- Invariant name --> <td>Knotilus URL</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>KnotilusURL</td>
<!-- KnotTheory = --> <td>KnotilusURL</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Navigation</td>
<!-- Type = --> <td>Navigation</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Next Knot</td>
<!-- Invariant name --> <td>Next Knot</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>NextKnot</td>
<!-- KnotTheory = --> <td>NextKnot</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>Knot</td>
<!-- ReadWiki = --> <td>Knot</td>
<!-- Type = --> <td>Navigation</td>
<!-- Type = --> <td>Navigation</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Previous Knot</td>
<!-- Invariant name --> <td>Previous Knot</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>PreviousKnot</td>
<!-- KnotTheory = --> <td>PreviousKnot</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>Knot</td>
<!-- ReadWiki = --> <td>Knot</td>
<!-- Type = --> <td>Navigation</td>
<!-- Type = --> <td>Navigation</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Gauss Code</td>
<!-- Invariant name --> <td>Gauss Code</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>GaussCode</td>
<!-- KnotTheory = --> <td>GaussCode</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>GaussCode</td>
<!-- ReadWiki = --> <td>GaussCode</td>
<!-- Type = --> <td>Link Presentation</td>
<!-- Type = --> <td>Link Presentation</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Planar Diagram</td>
<!-- Invariant name --> <td>Planar Diagram</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>PD</td>
<!-- KnotTheory = --> <td>PD</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>PD</td>
<!-- ReadWiki = --> <td>PD</td>
<!-- Type = --> <td>Link Presentation</td>
<!-- Type = --> <td>Link Presentation</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Dowker-Thistlethwaite Code</td>
<!-- Invariant name --> <td>Dowker-Thistlethwaite Code</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>DTCode</td>
<!-- KnotTheory = --> <td>DTCode</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>DTCode</td>
<!-- ReadWiki = --> <td>DTCode</td>
<!-- Type = --> <td>Knot Presentation</td>
<!-- Type = --> <td>Knot Presentation</td>
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<tr>
<tr>
<!-- Invariant name --> <td>SymmetryType</td>
<!-- Invariant name --> <td>SymmetryType</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>SymmetryType</td>
<!-- KnotTheory = --> <td>SymmetryType</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>SymmetryType</td>
<!-- ReadWiki = --> <td>SymmetryType</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>UnknottingNumber</td>
<!-- Invariant name --> <td>UnknottingNumber</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>UnknottingNumber</td>
<!-- KnotTheory = --> <td>UnknottingNumber</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>ThreeGenus</td>
<!-- Invariant name --> <td>ThreeGenus</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>ThreeGenus</td>
<!-- KnotTheory = --> <td>ThreeGenus</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>BridgeIndex</td>
<!-- Invariant name --> <td>BridgeIndex</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>BridgeIndex</td>
<!-- KnotTheory = --> <td>BridgeIndex</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>SuperBridgeIndex</td>
<!-- Invariant name --> <td>SuperBridgeIndex</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>SuperBridgeIndex</td>
<!-- KnotTheory = --> <td>SuperBridgeIndex</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>NakanishiIndex</td>
<!-- Invariant name --> <td>NakanishiIndex</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>NakanishiIndex</td>
<!-- KnotTheory = --> <td>NakanishiIndex</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Jones</td>
<!-- Invariant name --> <td>Jones</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Jones[#1][q] & </td>
<!-- KnotTheory = --> <td>Jones[#1][q] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Alexander</td>
<!-- Invariant name --> <td>Alexander</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Alexander[#1][t] & </td>
<!-- KnotTheory = --> <td>Alexander[#1][t] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Determinant</td>
<!-- Invariant name --> <td>Determinant</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>KnotDet</td>
<!-- KnotTheory = --> <td>KnotDet</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Signature</td>
<!-- Invariant name --> <td>Signature</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>KnotSignature</td>
<!-- KnotTheory = --> <td>KnotSignature</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Conway</td>
<!-- Invariant name --> <td>Conway</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Conway[#1][z] & </td>
<!-- KnotTheory = --> <td>Conway[#1][z] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>HOMFLYPT</td>
<!-- Invariant name --> <td>HOMFLYPT</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>HOMFLYPT[#1][a, z] & </td>
<!-- KnotTheory = --> <td>HOMFLYPT[#1][a, z] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Kauffman</td>
<!-- Invariant name --> <td>Kauffman</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Kauffman[#1][a, z] & </td>
<!-- KnotTheory = --> <td>Kauffman[#1][a, z] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Vassiliev2</td>
<!-- Invariant name --> <td>Vassiliev2</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Vassiliev[2]</td>
<!-- KnotTheory = --> <td>Vassiliev[2]</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Vassiliev Invariant</td>
<!-- Type = --> <td>Vassiliev Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Vassiliev3</td>
<!-- Invariant name --> <td>Vassiliev3</td>
⚫
<!-- KnotInfoTag = --> <td></td>
<!-- KnotTheory = --> <td>Vassiliev[3]</td>
<!-- KnotTheory = --> <td>Vassiliev[3]</td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Vassiliev Invariant</td>
<!-- Type = --> <td>Vassiliev Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Smooth 4-Genus</td>
<!-- Invariant name --> <td>Smooth 4-Genus</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- KnotInfoTag = --> <td>smooth_4_genus</td>
<!-- KnotInfoTag = --> <td>smooth_4_genus</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>4D Invariant</td>
<!-- Type = --> <td>4D Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Topological 4-Genus</td>
<!-- Invariant name --> <td>Topological 4-Genus</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- KnotInfoTag = --> <td>topological_4_genus</td>
<!-- KnotInfoTag = --> <td>topological_4_genus</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>4D Invariant</td>
<!-- Type = --> <td>4D Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Thurston-Bennequin Number</td>
<!-- Invariant name --> <td>Thurston-Bennequin Number</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- KnotInfoTag = --> <td>thurston_bennequin_number</td>
<!-- KnotInfoTag = --> <td>thurston_bennequin_number</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Hyperbolic Volume</td>
<!-- Invariant name --> <td>Hyperbolic Volume</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- KnotInfoTag = --> <td>volume</td>
<!-- KnotInfoTag = --> <td>volume</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Hyperbolic Invariant</td>
<!-- Type = --> <td>Hyperbolic Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Conway Notation</td>
<!-- Invariant name --> <td>Conway Notation</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- KnotInfoTag = --> <td>conway_notation</td>
<!-- KnotInfoTag = --> <td>conway_notation</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Knot Presentation</td>
<!-- Type = --> <td>Knot Presentation</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Concordance Order</td>
<!-- Invariant name --> <td>Concordance Order</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- KnotInfoTag = --> <td>concordance_order</td>
<!-- KnotInfoTag = --> <td>concordance_order</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Concordance Invariant</td>
<!-- Type = --> <td>Concordance Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Algebraic Concordance Order</td>
<!-- Invariant name --> <td>Algebraic Concordance Order</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- KnotInfoTag = --> <td>concordance_order_algebraic</td>
<!-- KnotInfoTag = --> <td>concordance_order_algebraic</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>Concordance Invariant</td>
<!-- Type = --> <td>Concordance Invariant</td>
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<tr>
<tr>
<!-- Invariant name --> <td>Ozsvath-Szabo Tau Invariant</td>
<!-- Invariant name --> <td>Ozsvath-Szabo Tau Invariant</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- KnotInfoTag = --> <td>ozsvath_szabo_tau</td>
<!-- KnotInfoTag = --> <td>ozsvath_szabo_tau</td>
⚫
<!-- KnotTheory = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- ReadWiki = --> <td></td>
<!-- Type = --> <td>4D Invariant</td>
<!-- Type = --> <td>4D Invariant</td>

Revision as of 19:50, 1 November 2005

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 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
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
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