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=== Modifying This Page === |
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|align=left|'''Read me first:''' [[Modifying Knot Pages]] |
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See/edit the [[Template:Link Page|Link Page]] master template (intermediate). |
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See/edit the [[Link_Splice_Base]] (expert). |
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Back to the [[#top|top]]. |
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|align=right|{{Knot Navigation Links|ext=gif}} |
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[[Category:Knot Page]] |
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Revision as of 22:38, 21 August 2007
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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 (Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings).
Visit [{{{KnotilusURL}}} Link Page's page] at Knotilus. Visit Link Page's page at the original Knot Atlas. |
Link Presentations
[edit Notes on Link Page's Link Presentations]
| Planar diagram presentation | Data:Link Page/PD Presentation |
| Gauss code | Data:Link Page/Gauss Code |
| A Braid Representative | {{{braid_table}}} |
| A Morse Link Presentation | File:Link Page ML.gif |
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) |
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.
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