K11n116

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K11n115.gif

K11n115

K11n117.gif

K11n117

K11n116.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n116 at Knotilus!


K11n116 is not -colourable for any . See The Determinant and the Signature.

Knot presentations

Planar diagram presentation X4251 X10,3,11,4 X5,14,6,15 X7,19,8,18 X9,17,10,16 X2,11,3,12 X20,13,21,14 X15,22,16,1 X17,9,18,8 X12,19,13,20 X21,7,22,6
Gauss code 1, -6, 2, -1, -3, 11, -4, 9, -5, -2, 6, -10, 7, 3, -8, 5, -9, 4, 10, -7, -11, 8
Dowker-Thistlethwaite code 4 10 -14 -18 -16 2 20 -22 -8 12 -6
A Braid Representative {{{braid_table}}}
A Morse Link Presentation K11n116 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:K11n116/ThurstonBennequinNumber
Hyperbolic Volume 7.75445
A-Polynomial See Data:K11n116/A-polynomial

[edit Notes for K11n116's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11n116's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
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 Data:K11n116/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n116/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11n49,}

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

Vassiliev invariants

V2 and V3: (-4, 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 K11n116. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-6-5-4-3-2-101234χ
7          11
5           0
3        11 0
1      21   1
-1      11   0
-3    121    0
-5   1       -1
-7   11      0
-9 11        0
-11           0
-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).

Back to the top.

K11n115.gif

K11n115

K11n117.gif

K11n117