10 53
From Knot Atlas
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See the full Rolfsen Knot Table. Visit 10 53's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X1425 X3849 X5,14,6,15 X15,20,16,1 X9,16,10,17 X19,10,20,11 X11,18,12,19 X17,12,18,13 X13,6,14,7 X7283 |
Gauss code | -1, 10, -2, 1, -3, 9, -10, 2, -5, 6, -7, 8, -9, 3, -4, 5, -8, 7, -6, 4 |
Dowker-Thistlethwaite code | 4 8 14 2 16 18 6 20 12 10 |
Conway Notation | [311,21,2] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 12, width is 5, Braid index is 5 |
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![]() [{12, 6}, {5, 10}, {8, 11}, {10, 12}, {9, 7}, {6, 8}, {7, 1}, {11, 4}, {3, 5}, {4, 2}, {1, 3}, {2, 9}] |
[edit Notes on presentations of 10 53]
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: {K11a95,}
Same Jones Polynomial (up to mirroring, ): {}
Vassiliev invariants
V2 and V3: | (6, -13) |
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 53. 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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