K11n111

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K11n110.gif

K11n110

K11n112.gif

K11n112

K11n111.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n111 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X10,3,11,4 X5,14,6,15 X7,17,8,16 X9,19,10,18 X2,11,3,12 X13,21,14,20 X15,22,16,1 X17,9,18,8 X19,13,20,12 X21,7,22,6
Gauss code 1, -6, 2, -1, -3, 11, -4, 9, -5, -2, 6, 10, -7, 3, -8, 4, -9, 5, -10, 7, -11, 8
Dowker-Thistlethwaite code 4 10 -14 -16 -18 2 -20 -22 -8 -12 -6
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gif
A Morse Link Presentation K11n111 ML.gif

Four dimensional invariants

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

[edit Notes for K11n111's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 7, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant Data:K11n111/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, -2)
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 K11n111. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-4-3-2-10123456χ
15          11
13         1 -1
11        11 0
9      121  0
7      11   0
5    122    1
3   111     -1
1   12      1
-1 11        0
-3           0
-51          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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K11n110.gif

K11n110

K11n112.gif

K11n112