Template:Link Page

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Knot presentations

Planar diagram presentation	Data:Link Page/PD Presentation
Gauss code	Data:Link Page/Gauss Code
A Morse Link Presentation	File:Link Page ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...)	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:

V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9 Data:Link Page/V 2,1 Data:Link Page/V 3,1 Data:Link Page/V 4,1 Data:Link Page/V 4,2 Data:Link Page/V 4,3 Data:Link Page/V 5,1 Data:Link Page/V 5,2 Data:Link Page/V 5,3 Data:Link Page/V 5,4 Data:Link Page/V 6,1 Data:Link Page/V 6,2 Data:Link Page/V 6,3 Data:Link Page/V 6,4 Data:Link Page/V 6,5 Data:Link Page/V 6,6 Data:Link Page/V 6,7 Data:Link Page/V 6,8 Data:Link Page/V 6,9

V_2,1 through V_6,9 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 $t^{r}q^{j}$ are shown, along with their alternating sums $\chi$ (fixed $j$, alternation over $r$). The squares with yellow highlighting are those on the "critical diagonals", where $j-2r=s+1$ or $j-2r=s-1$, where $s=$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}}}

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