K11n34

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K11n33.gif

K11n33

K11n35.gif

K11n35

K11n34.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n34 at Knotilus!

K11n34 is the mirror of the "Conway" knot; it is a mutant of the (mirror of the) Kinoshita-Terasaka knot K11n42. See also Heegaard Floer Knot Homology.


K11n34 is not -colourable for any . See The Determinant and the Signature.

Gateknot.jpg Knot emblem on the closed gate of the mathematics department at night. Cambridge, England. See also Heegaard Floer Knot Homology.
Knot K11n34.
A graph, knot K11n34.
A part of a knot and a part of a graph.

Knot presentations

Planar diagram presentation X4251 X8493 X12,5,13,6 X2837 X9,17,10,16 X11,18,12,19 X6,13,7,14 X15,20,16,21 X17,1,18,22 X19,14,20,15 X21,10,22,11
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.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart4.gif
A Morse Link Presentation K11n34 ML.gif

Four dimensional invariants

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

[edit Notes for K11n34's four dimensional invariants] By the theorem of M. Freedman, the topological 4-genus is zero, as the Alexander polynomial is one.

Polynomial invariants

Alexander polynomial 1
Conway polynomial 1
2nd Alexander ideal (db, data sources)
Determinant and Signature { 1, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant Data:K11n34/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {0_1, K11n42,}

Same Jones Polynomial (up to mirroring, ): {K11n42,}

Vassiliev invariants

V2 and V3: (0, 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 0 is the signature of K11n34. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-6-5-4-3-2-1012345χ
9           1-1
7          1 1
5         11 0
3       121  0
1      211   2
-1     132    0
-3    221     1
-5   111      -1
-7  121       0
-9 11         0
-11 1          -1
-131           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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K11n33.gif

K11n33

K11n35.gif

K11n35