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Visit [{{{KnotilusURL}}} Link Page's page] at Knotilus! Visit Template:N{{{t}}}{{{k}}}.html Link Page's page at the original Knot Atlas!|t={{{t}}}|k={{{k}}}|KnotilusURL={{{KnotilusURL}}}}} 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 $u$, $v$, $w$, ...) 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 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 $t^{r}q^{j}$ 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}}} See/edit the Link_Splice_Template. Back to the top. [[Image:Data:Link Page/Previous Knot.gif|80px|link=Data:Link Page/Previous Knot]] [[Data:Link Page/Previous Knot]] [[Image:Data:Link Page/Next Knot.gif|80px|link=Data:Link Page/Next Knot]] [[Data:Link Page/Next Knot]]