10 65
From Knot Atlas
Jump to navigationJump to search
|
|
![]() (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 65's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X1425 X3,10,4,11 X11,19,12,18 X5,15,6,14 X17,7,18,6 X7,17,8,16 X15,9,16,8 X13,1,14,20 X19,13,20,12 X9,2,10,3 |
Gauss code | -1, 10, -2, 1, -4, 5, -6, 7, -10, 2, -3, 9, -8, 4, -7, 6, -5, 3, -9, 8 |
Dowker-Thistlethwaite code | 4 10 14 16 2 18 20 8 6 12 |
Conway Notation | [31,3,21] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 11, width is 4, Braid index is 4 |
![]() |
![]() [{9, 2}, {1, 7}, {4, 8}, {7, 9}, {10, 13}, {8, 12}, {13, 11}, {3, 5}, {6, 4}, {5, 10}, {2, 6}, {12, 3}, {11, 1}] |
[edit Notes on presentations of 10 65]
Three dimensional invariants
|
Four dimensional invariants
|
Polynomial invariants
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {10_77, K11n71, K11n75,}
Same Jones Polynomial (up to mirroring, ): {}
Vassiliev invariants
V2 and V3: | (4, 7) |
V2,1 through V6,9: |
|
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 2 is the signature of 10 65. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
|
Integral Khovanov Homology
(db, data source) |
|