10 48: Difference between revisions
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See/edit the [[Rolfsen_Splice_Template]]. |
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Back to the [[#top|top]]. |
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[[Category:Knot Page]] |
[[Category:Knot Page]] |
Revision as of 20:01, 29 August 2005
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Visit 10 48's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)
Visit 10 48's page at Knotilus! Visit 10 48's page at the original Knot Atlas! |
Knot presentations
Planar diagram presentation | X6271 X8493 X14,6,15,5 X20,15,1,16 X16,9,17,10 X18,11,19,12 X10,17,11,18 X12,19,13,20 X2837 X4,14,5,13 |
Gauss code | 1, -9, 2, -10, 3, -1, 9, -2, 5, -7, 6, -8, 10, -3, 4, -5, 7, -6, 8, -4 |
Dowker-Thistlethwaite code | 6 8 14 2 16 18 4 20 10 12 |
Conway Notation | [41,3,2] |
Length is 10, width is 3. Braid index is 3. |
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, 0) |
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 0 is the signature of 10 48. 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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