Template:Link Page: Difference between revisions
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| valign="top" rowspan=2 | [[Image:{{PAGENAME}}.gif]] |
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| Visit [{{{KnotilusURL}}} {{PAGENAME}}'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]! |
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| {{Link Knot Site Links|n={{{n|t={{{t}}}|k={{{k}}}|KnotilusURL={{{KnotilusURL}}}}} |
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Visit [http://www.math.toronto.edu/~drorbn/KAtlas/Links/{{{n{{{t}}}{{{k}}}.html {{PAGENAME}}'s page] at the original [http://www.math.toronto.edu/~drorbn/KAtlas/index.html Knot Atlas]!}|t={{{t}}}|k={{{k}}}|KnotilusURL={{{KnotilusURL}}}}} |
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| valign="top" | {{:{{PAGENAME}} Quick Notes}} |
| valign="top" | {{:{{PAGENAME}} Quick Notes}} |
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Revision as of 12:16, 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!}|t={{{t}}}|k={{{k}}}|KnotilusURL={{{KnotilusURL}}}}} |
| 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_Splice_Template.
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