Invariant Definition Table: Difference between revisions

From Knot Atlas
Jump to navigationJump to search
No edit summary
No edit summary
Line 5: Line 5:
<th>KnotTheory</th>
<th>KnotTheory</th>
<th>LivingstonTag</th>
<th>LivingstonTag</th>
<th>ReadLivingston</th>
<th>ReadWiki</th>
<th>ReadWiki</th>
<th>Type</th>
<th>Type</th>
Line 13: Line 14:
<!-- KnotTheory = --> <td>NextKnot</td>
<!-- KnotTheory = --> <td>NextKnot</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>Knot</td>
<!-- ReadWiki = --> <td>Knot</td>
<!-- Type = --> <td>Navigation</td>
<!-- Type = --> <td>Navigation</td>
Line 21: Line 23:
<!-- KnotTheory = --> <td>PreviousKnot</td>
<!-- KnotTheory = --> <td>PreviousKnot</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>Knot</td>
<!-- ReadWiki = --> <td>Knot</td>
<!-- Type = --> <td>Navigation</td>
<!-- Type = --> <td>Navigation</td>
Line 29: Line 32:
<!-- KnotTheory = --> <td>GaussCode</td>
<!-- KnotTheory = --> <td>GaussCode</td>
<!-- LivingstonTag = --> <td></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>
Line 37: Line 41:
<!-- KnotTheory = --> <td>PD</td>
<!-- KnotTheory = --> <td>PD</td>
<!-- LivingstonTag = --> <td></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>
Line 45: Line 50:
<!-- KnotTheory = --> <td>DTCode</td>
<!-- KnotTheory = --> <td>DTCode</td>
<!-- LivingstonTag = --> <td></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>
Line 53: Line 59:
<!-- KnotTheory = --> <td>SymmetryType</td>
<!-- KnotTheory = --> <td>SymmetryType</td>
<!-- LivingstonTag = --> <td></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>
Line 61: Line 68:
<!-- KnotTheory = --> <td>UnknottingNumber</td>
<!-- KnotTheory = --> <td>UnknottingNumber</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
Line 69: Line 77:
<!-- KnotTheory = --> <td>ThreeGenus</td>
<!-- KnotTheory = --> <td>ThreeGenus</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
Line 77: Line 86:
<!-- KnotTheory = --> <td>BridgeIndex</td>
<!-- KnotTheory = --> <td>BridgeIndex</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
Line 85: Line 95:
<!-- KnotTheory = --> <td>SuperBridgeIndex</td>
<!-- KnotTheory = --> <td>SuperBridgeIndex</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
Line 93: Line 104:
<!-- KnotTheory = --> <td>NakanishiIndex</td>
<!-- KnotTheory = --> <td>NakanishiIndex</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>3D Invariant</td>
<!-- Type = --> <td>3D Invariant</td>
Line 101: Line 113:
<!-- KnotTheory = --> <td>Jones[#1][q] & </td>
<!-- KnotTheory = --> <td>Jones[#1][q] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
Line 109: Line 122:
<!-- KnotTheory = --> <td>Alexander[#1][t] & </td>
<!-- KnotTheory = --> <td>Alexander[#1][t] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
Line 117: Line 131:
<!-- KnotTheory = --> <td>KnotDet</td>
<!-- KnotTheory = --> <td>KnotDet</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
Line 125: Line 140:
<!-- KnotTheory = --> <td>KnotSignature</td>
<!-- KnotTheory = --> <td>KnotSignature</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
Line 133: Line 149:
<!-- KnotTheory = --> <td>Conway[#1][z] & </td>
<!-- KnotTheory = --> <td>Conway[#1][z] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
Line 141: Line 158:
<!-- KnotTheory = --> <td>HOMFLYPT[#1][a, z] & </td>
<!-- KnotTheory = --> <td>HOMFLYPT[#1][a, z] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
Line 149: Line 167:
<!-- KnotTheory = --> <td>Kauffman[#1][a, z] & </td>
<!-- KnotTheory = --> <td>Kauffman[#1][a, z] & </td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Polynomial Invariant</td>
<!-- Type = --> <td>Polynomial Invariant</td>
Line 157: Line 176:
<!-- KnotTheory = --> <td>Vassiliev[2]</td>
<!-- KnotTheory = --> <td>Vassiliev[2]</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Vassiliev Invariant</td>
<!-- Type = --> <td>Vassiliev Invariant</td>
Line 165: Line 185:
<!-- KnotTheory = --> <td>Vassiliev[3]</td>
<!-- KnotTheory = --> <td>Vassiliev[3]</td>
<!-- LivingstonTag = --> <td></td>
<!-- LivingstonTag = --> <td></td>
<!-- ReadLivingston = --> <td></td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- ReadWiki = --> <td>FromWikiString</td>
<!-- Type = --> <td>Vassiliev Invariant</td>
<!-- Type = --> <td>Vassiliev Invariant</td>

Revision as of 01:02, 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 FromWikiString 3D Invariant Unknotting_Number
ThreeGenus ThreeGenus FromWikiString 3D Invariant 3-Genus
BridgeIndex BridgeIndex FromWikiString 3D Invariant Bridge_Index
SuperBridgeIndex SuperBridgeIndex FromWikiString 3D Invariant Super_Bridge_Index
NakanishiIndex NakanishiIndex FromWikiString 3D Invariant Nakanishi_Index
Jones Jones[#1][q] & FromWikiString Polynomial Invariant Jones_Polynomial
Alexander Alexander[#1][t] & FromWikiString Polynomial Invariant Alexander_Polynomial
Determinant KnotDet FromWikiString Polynomial Invariant Determinant
Signature KnotSignature FromWikiString Polynomial Invariant Signature
Conway Conway[#1][z] & FromWikiString Polynomial Invariant Conway_Polynomial
HOMFLYPT HOMFLYPT[#1][a, z] & FromWikiString Polynomial Invariant HOMFLYPT_Polynomial
Kauffman Kauffman[#1][a, z] & FromWikiString Polynomial Invariant Kauffman_Polynomial
Vassiliev2 Vassiliev[2] FromWikiString Vassiliev Invariant V_2
Vassiliev3 Vassiliev[3] FromWikiString Vassiliev Invariant V_3
Smooth 4-Genus smooth_4_genus FromLivingstonString FromWikiString 4D Invariant Smooth4Genus
Topological 4-Genus topological_4_genus FromLivingstonString FromWikiString 4D Invariant Topological4Genus
Thurston-Bennequin Number thurston_bennequin_number (ToExpression/@StringCases[#,"["~~a__~~"]:>a]&) FromWikiString 3D Invariant ThurstonBennequinNumber
Retrieved from "https://katlas.org/index.php?title=Invariant_Definition_Table&oldid=48203"