K11a11

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K11a10.gif

K11a10

K11a12.gif

K11a12

K11a11.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a11 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8394 X10,6,11,5 X16,8,17,7 X2,9,3,10 X20,11,21,12 X18,14,19,13 X6,16,7,15 X14,18,15,17 X22,19,1,20 X12,21,13,22
Gauss code 1, -5, 2, -1, 3, -8, 4, -2, 5, -3, 6, -11, 7, -9, 8, -4, 9, -7, 10, -6, 11, -10
Dowker-Thistlethwaite code 4 8 10 16 2 20 18 6 14 22 12
A Braid Representative
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BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
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A Morse Link Presentation K11a11 ML.gif

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant 0

[edit Notes for K11a11's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 113, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a11/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a11/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a167,}

Same Jones Polynomial (up to mirroring, ): {K11a167,}

Vassiliev invariants

V2 and V3: (0, -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 0 is the signature of K11a11. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-5-4-3-2-10123456χ
13           11
11          3 -3
9         51 4
7        73  -4
5       95   4
3      97    -2
1     99     0
-1    710      3
-3   48       -4
-5  27        5
-7 14         -3
-9 2          2
-111           -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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K11a10.gif

K11a10

K11a12.gif

K11a12