K11n150

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K11n149.gif

K11n149

K11n151.gif

K11n151

K11n150.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n150 at Knotilus!



Knot presentations

Planar diagram presentation X6271 X8394 X10,6,11,5 X18,8,19,7 X16,9,17,10 X11,1,12,22 X13,21,14,20 X4,16,5,15 X2,17,3,18 X19,15,20,14 X21,13,22,12
Gauss code 1, -9, 2, -8, 3, -1, 4, -2, 5, -3, -6, 11, -7, 10, 8, -5, 9, -4, -10, 7, -11, 6
Dowker-Thistlethwaite code 6 8 10 18 16 -22 -20 4 2 -14 -12
A Braid Representative
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A Morse Link Presentation K11n150 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11n150/ThurstonBennequinNumber
Hyperbolic Volume 14.7873
A-Polynomial See Data:K11n150/A-polynomial

[edit Notes for K11n150's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant -2

[edit Notes for K11n150's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 75, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n150/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n150/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a258,}

Same Jones Polynomial (up to mirroring, ): {K11n66,}

Vassiliev invariants

V2 and V3: (-1, -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 2 is the signature of K11n150. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-3-2-10123456χ
15         22
13        3 -3
11       52 3
9      73  -4
7     65   1
5    67    1
3   56     -1
1  37      4
-1 14       -3
-3 3        3
-51         -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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K11n149.gif

K11n149

K11n151.gif

K11n151