K11a70

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K11a69.gif

K11a69

K11a71.gif

K11a71

K11a70.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a70 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8394 X18,6,19,5 X12,8,13,7 X2,9,3,10 X16,11,17,12 X20,14,21,13 X6,16,7,15 X10,17,11,18 X22,20,1,19 X14,22,15,21
Gauss code 1, -5, 2, -1, 3, -8, 4, -2, 5, -9, 6, -4, 7, -11, 8, -6, 9, -3, 10, -7, 11, -10
Dowker-Thistlethwaite code 4 8 18 12 2 16 20 6 10 22 14
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gif
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A Morse Link Presentation K11a70 ML.gif

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant -2

[edit Notes for K11a70's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 151, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a70/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a70/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, ): {}

Vassiliev invariants

V2 and V3: (-2, -1)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 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 K11a70. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-4-3-2-101234567χ
17           1-1
15          4 4
13         71 -6
11        104  6
9       127   -5
7      1310    3
5     1112     1
3    913      -4
1   612       6
-1  28        -6
-3 16         5
-5 2          -2
-71           1
Integral Khovanov Homology

(db, data source)

  

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 Hoste-Thistlethwaite Knot Page master template (intermediate).

See/edit the Hoste-Thistlethwaite_Splice_Base (expert).

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K11a69.gif

K11a69

K11a71.gif

K11a71