K11n35

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K11n34.gif

K11n34

K11n36.gif

K11n36

K11n35.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n35 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8493 X5,13,6,12 X2837 X16,9,17,10 X18,12,19,11 X13,7,14,6 X20,16,21,15 X22,17,1,18 X14,20,15,19 X10,22,11,21
Gauss code 1, -4, 2, -1, -3, 7, 4, -2, 5, -11, 6, 3, -7, -10, 8, -5, 9, -6, 10, -8, 11, -9
Dowker-Thistlethwaite code 4 8 -12 2 16 18 -6 20 22 14 10
A Braid Representative
BraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart2.gifBraidPart2.gifBraidPart1.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart2.gif
A Morse Link Presentation K11n35 ML.gif

Four dimensional invariants

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

[edit Notes for K11n35's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 89, 4 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant Data:K11n35/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {10_92, K11a153, K11a224, K11n43,}

Same Jones Polynomial (up to mirroring, ): {K11n43,}

Vassiliev invariants

V2 and V3: (2, 3)
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 4 is the signature of K11n35. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
0123456789χ
23         1-1
21        3 3
19       51 -4
17      73  4
15     85   -3
13    77    0
11   78     1
9  47      -3
7 27       5
514        -3
33         3
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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K11n34.gif

K11n34

K11n36.gif

K11n36