K11n132

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K11n131.gif

K11n131

K11n133.gif

K11n133

K11n132.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X4251 X10,3,11,4 X5,19,6,18 X7,16,8,17 X9,14,10,15 X2,11,3,12 X13,20,14,21 X15,8,16,9 X17,1,18,22 X19,12,20,13 X21,7,22,6
Gauss code 1, -6, 2, -1, -3, 11, -4, 8, -5, -2, 6, 10, -7, 5, -8, 4, -9, 3, -10, 7, -11, 9
Dowker-Thistlethwaite code 4 10 -18 -16 -14 2 -20 -8 -22 -12 -6
A Braid Representative
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A Morse Link Presentation K11n132 ML.gif

Three dimensional invariants

Symmetry type Chiral
Unknotting number
3-genus 2
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11n132/ThurstonBennequinNumber
Hyperbolic Volume 10.2668
A-Polynomial See Data:K11n132/A-polynomial

[edit Notes for K11n132's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11n132's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 25, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n132/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n132/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {8_8, 10_129, K11n39, K11n45, K11n50,}

Same Jones Polynomial (up to mirroring, ): {K11n50, K11n133,}

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 0 is the signature of K11n132. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-7-6-5-4-3-2-101χ
3        1-1
1       2 2
-1      22 0
-3     21  1
-5    22   0
-7   22    0
-9  12     1
-11 12      -1
-13 1       1
-151        -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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K11n131.gif

K11n131

K11n133.gif

K11n133