T(7,4): Difference between revisions
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{{Torus Knot Page| |
{{Torus Knot Page| |
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m = 7 | |
m = 7 | |
Latest revision as of 10:37, 31 August 2005
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See other torus knots |
Edit T(7,4) Quick Notes
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Edit T(7,4) Further Notes and Views
Knot presentations
Planar diagram presentation | X9,41,10,40 X20,42,21,41 X31,1,32,42 X21,11,22,10 X32,12,33,11 X1,13,2,12 X33,23,34,22 X2,24,3,23 X13,25,14,24 X3,35,4,34 X14,36,15,35 X25,37,26,36 X15,5,16,4 X26,6,27,5 X37,7,38,6 X27,17,28,16 X38,18,39,17 X7,19,8,18 X39,29,40,28 X8,30,9,29 X19,31,20,30 |
Gauss code | -6, -8, -10, 13, 14, 15, -18, -20, -1, 4, 5, 6, -9, -11, -13, 16, 17, 18, -21, -2, -4, 7, 8, 9, -12, -14, -16, 19, 20, 21, -3, -5, -7, 10, 11, 12, -15, -17, -19, 1, 2, 3 |
Dowker-Thistlethwaite code | 12 34 -26 18 40 -32 24 4 -38 30 10 -2 36 16 -8 42 22 -14 6 28 -20 |
Braid presentation |
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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: | (30, 140) |
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 14 is the signature of T(7,4). 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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Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`
. See A Sample KnotTheory` Session.
Modifying This Page
Read me first: Modifying Knot Pages
See/edit the Torus Knot Page master template (intermediate). See/edit the Torus Knot_Splice_Base (expert). Back to the top. |
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