10 61: Difference between revisions
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See/edit the [[Rolfsen_Splice_Template]]. |
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[[Category:Knot Page]] |
[[Category:Knot Page]] |
Revision as of 21:07, 29 August 2005
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Visit 10 61's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)
Visit 10 61's page at Knotilus! Visit 10 61's page at the original Knot Atlas! 10_61 is also known as the pretzel knot P(4,3,3). |
Knot presentations
Planar diagram presentation | X8291 X10,4,11,3 X2,10,3,9 X18,12,19,11 X14,7,15,8 X16,5,17,6 X6,15,7,16 X4,17,5,18 X20,14,1,13 X12,20,13,19 |
Gauss code | 1, -3, 2, -8, 6, -7, 5, -1, 3, -2, 4, -10, 9, -5, 7, -6, 8, -4, 10, -9 |
Dowker-Thistlethwaite code | 8 10 16 14 2 18 20 6 4 12 |
Conway Notation | [4,3,3] |
Length is 11, width is 4. Braid index is 4. |
Three dimensional invariants
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Four dimensional invariants
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Polynomial invariants
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {...}
Same Jones Polynomial (up to mirroring, ): {...}
Vassiliev invariants
V2 and V3: | (-4, -5) |
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 are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where 4 is the signature of 10 61. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
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Integral Khovanov Homology
(db, data source) |
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