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===Knot presentations=== |
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|'''[[Planar Diagrams|Planar diagram presentation]]''' |
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|style="padding-left: 1em; word-wrap: break-word" | {{Data:{{PAGENAME}}/PD Presentation}} |
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|'''[[Gauss Codes|Gauss code]]''' |
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|style="padding-left: 1em; word-wrap: break-word" | {{Data:{{PAGENAME}}/Gauss Code}} |
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{{Link Presentations}} |
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{{Link Polynomial Invariants}} |
{{Link Polynomial Invariants}} |
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{{Vassiliev Invariants}} |
{{Vassiliev Invariants}} |
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|align=left|See/edit the [[Template:Link Page|Link Page]] template. |
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See/edit the [[Link_Splice__Base]]. |
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|align=right|{{Knot Navigation Links|ext=gif}} |
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Revision as of 21:10, 30 August 2005
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[[Image:Data:Link Page/Previous Knot.gif|80px|link=Data:Link Page/Previous Knot]] |
[[Image:Data:Link Page/Next Knot.gif|80px|link=Data:Link Page/Next Knot]] |
| File:Link Page.gif | Visit [{{{KnotilusURL}}} Link Page's page] at Knotilus!
Visit Link Page's page at the original Knot Atlas! |
| Link Page Quick Notes |
Link Page Further Notes and Views
Knot presentations
| Planar diagram presentation | Data:Link Page/PD Presentation |
| Gauss code | Data:Link Page/Gauss Code |
Polynomial invariants
| Multivariable Alexander Polynomial (in [math]\displaystyle{ u }[/math], [math]\displaystyle{ v }[/math], [math]\displaystyle{ w }[/math], ...) | Data:Link Page/Multivariable Alexander (db) |
| Jones polynomial | Data:Link Page/Jones Polynomial (db) |
| Signature | Data:Link Page/Signature (db) |
| HOMFLY-PT polynomial | Data:Link Page/HOMFLYPT Polynomial (db) |
| Kauffman polynomial | Data:Link Page/Kauffman Polynomial (db) |
Vassiliev invariants
| V2 and V3: | (Data:Link Page/V 2, Data:Link Page/V 3) |
| V2,1 through V6,9: |
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V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
| The coefficients of the monomials [math]\displaystyle{ t^rq^j }[/math] are shown, along with their alternating sums [math]\displaystyle{ \chi }[/math] (fixed [math]\displaystyle{ j }[/math], alternation over [math]\displaystyle{ r }[/math]). The squares with yellow highlighting are those on the "critical diagonals", where [math]\displaystyle{ j-2r=s+1 }[/math] or [math]\displaystyle{ j-2r=s-1 }[/math], where [math]\displaystyle{ s= }[/math]Data:Link Page/Signature is the signature of Link Page. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:Link Page/KhovanovTable |
| Integral Khovanov Homology
(db, data source) |
Data:Link Page/Integral Khovanov Homology |
Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.
{{{computer_talk}}}
| See/edit the Link Page template.
See/edit the Link_Splice__Base. Back to the top. |
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| See/edit the Template.
Back to the top. |
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