Invariant Definition Table: Difference between revisions

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<!-- LivingstonTag = --> <td></td>
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<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- WikiPage = --> <td>Unknotting_Number</td>
<!-- WikiPage = --> <td>Unknotting_Number</td>
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<!-- LivingstonTag = --> <td></td>
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<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- WikiPage = --> <td>3-Genus</td>
<!-- WikiPage = --> <td>3-Genus</td>
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<!-- LivingstonTag = --> <td></td>
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<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- WikiPage = --> <td>Bridge_Index</td>
<!-- WikiPage = --> <td>Bridge_Index</td>
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<!-- LivingstonTag = --> <td></td>
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<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- WikiPage = --> <td>Super_Bridge_Index</td>
<!-- WikiPage = --> <td>Super_Bridge_Index</td>
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<!-- LivingstonTag = --> <td></td>
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<!-- ReadLivingston = --> <td></td>
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<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- WikiPage = --> <td>Nakanishi_Index</td>
<!-- WikiPage = --> <td>Nakanishi_Index</td>
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<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- WikiPage = --> <td>Jones_Polynomial</td>
<!-- WikiPage = --> <td>Jones_Polynomial</td>
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<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- WikiPage = --> <td>Alexander_Polynomial</td>
<!-- WikiPage = --> <td>Alexander_Polynomial</td>
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<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- WikiPage = --> <td>Determinant</td>
<!-- WikiPage = --> <td>Determinant</td>
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<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- WikiPage = --> <td>Signature</td>
<!-- WikiPage = --> <td>Signature</td>
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<!-- LivingstonTag = --> <td></td>
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<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- WikiPage = --> <td>Conway_Polynomial</td>
<!-- WikiPage = --> <td>Conway_Polynomial</td>
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<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- WikiPage = --> <td>HOMFLYPT_Polynomial</td>
<!-- WikiPage = --> <td>HOMFLYPT_Polynomial</td>
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<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- WikiPage = --> <td>Kauffman_Polynomial</td>
<!-- WikiPage = --> <td>Kauffman_Polynomial</td>
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<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Vassiliev Invariant</td>
<!-- Type = --> <td>Vassiliev Invariant</td>
<!-- WikiPage = --> <td>V_2</td>
<!-- WikiPage = --> <td>V_2</td>
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<!-- LivingstonTag = --> <td></td>
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<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Vassiliev Invariant</td>
<!-- Type = --> <td>Vassiliev Invariant</td>
<!-- WikiPage = --> <td>V_3</td>
<!-- WikiPage = --> <td>V_3</td>
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<!-- LivingstonTag = --> <td>smooth_4_genus</td>
<!-- LivingstonTag = --> <td>smooth_4_genus</td>
<!-- ReadLivingston = --> <td>FromLivingstonString</td>
<!-- ReadLivingston = --> <td>FromLivingstonString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>4D Invariant</td>
<!-- Type = --> <td>4D Invariant</td>
<!-- WikiPage = --> <td>Smooth4Genus</td>
<!-- WikiPage = --> <td>Smooth4Genus</td>
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<!-- LivingstonTag = --> <td>topological_4_genus</td>
<!-- LivingstonTag = --> <td>topological_4_genus</td>
<!-- ReadLivingston = --> <td>FromLivingstonString</td>
<!-- ReadLivingston = --> <td>FromLivingstonString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>4D Invariant</td>
<!-- Type = --> <td>4D Invariant</td>
<!-- WikiPage = --> <td>Topological4Genus</td>
<!-- WikiPage = --> <td>Topological4Genus</td>
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<!-- LivingstonTag = --> <td>thurston_bennequin_number</td>
<!-- LivingstonTag = --> <td>thurston_bennequin_number</td>
<!-- ReadLivingston = --> <td>(ToExpression/@StringCases[#,"["~~a__~~"]:>a]&)</td>
<!-- ReadLivingston = --> <td>(ToExpression/@StringCases[#,"["~~a__~~"]:>a]&)</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- WikiPage = --> <td>ThurstonBennequinNumber</td>
<!-- WikiPage = --> <td>ThurstonBennequinNumber</td>

Revision as of 01:08, 6 September 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 KnotTheory LivingstonTag ReadLivingston ReadWiki Type WikiPage
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 FromLivingstonString 4D Invariant Smooth4Genus
Topological 4-Genus topological_4_genus FromLivingstonString 4D Invariant Topological4Genus
Thurston-Bennequin Number thurston_bennequin_number (ToExpression/@StringCases[#,"["~~a__~~"]:>a]&) 3D Invariant ThurstonBennequinNumber
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