10 101
From Knot Atlas
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(KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 101's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X4251 X10,4,11,3 X14,6,15,5 X20,16,1,15 X16,12,17,11 X12,20,13,19 X18,8,19,7 X6,14,7,13 X8,18,9,17 X2,10,3,9 |
Gauss code | 1, -10, 2, -1, 3, -8, 7, -9, 10, -2, 5, -6, 8, -3, 4, -5, 9, -7, 6, -4 |
Dowker-Thistlethwaite code | 4 10 14 18 2 16 6 20 8 12 |
Conway Notation | [21:2:2] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 14, width is 5, Braid index is 5 |
[{3, 9}, {2, 5}, {1, 3}, {10, 7}, {8, 6}, {7, 4}, {9, 11}, {5, 10}, {12, 8}, {11, 2}, {4, 12}, {6, 1}] |
[edit Notes on presentations of 10 101]
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: {K11a200,}
Same Jones Polynomial (up to mirroring, ): {}
Vassiliev invariants
V2 and V3: | (7, 17) |
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 10 101. 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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