K11n79

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K11n78.gif

K11n78

K11n80.gif

K11n80

K11n79.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X4251 X8493 X5,14,6,15 X2837 X9,21,10,20 X11,19,12,18 X13,6,14,7 X15,22,16,1 X17,13,18,12 X19,11,20,10 X21,16,22,17
Gauss code 1, -4, 2, -1, -3, 7, 4, -2, -5, 10, -6, 9, -7, 3, -8, 11, -9, 6, -10, 5, -11, 8
Dowker-Thistlethwaite code 4 8 -14 2 -20 -18 -6 -22 -12 -10 -16
A Braid Representative
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A Morse Link Presentation K11n79 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 2
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11n79/ThurstonBennequinNumber
Hyperbolic Volume 6.75197
A-Polynomial See Data:K11n79/A-polynomial

[edit Notes for K11n79's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11n79's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 15, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n79/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n79/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11n138,}

Same Jones Polynomial (up to mirroring, ): {K11n138,}

Vassiliev invariants

V2 and V3: (-4, -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 K11n79. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-4-3-2-101234χ
11        11
9         0
7      21 1
5     1   -1
3    12   -1
1   22    0
-1   11    0
-3 12      1
-5         0
-71        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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K11n78.gif

K11n78

K11n80.gif

K11n80