K11n99

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K11n98.gif

K11n98

K11n100.gif

K11n100

K11n99.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n99 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X10,3,11,4 X5,14,6,15 X7,12,8,13 X9,19,10,18 X2,11,3,12 X13,6,14,7 X15,20,16,21 X17,22,18,1 X19,9,20,8 X21,16,22,17
Gauss code 1, -6, 2, -1, -3, 7, -4, 10, -5, -2, 6, 4, -7, 3, -8, 11, -9, 5, -10, 8, -11, 9
Dowker-Thistlethwaite code 4 10 -14 -12 -18 2 -6 -20 -22 -8 -16
A Braid Representative
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A Morse Link Presentation K11n99 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:K11n99/ThurstonBennequinNumber
Hyperbolic Volume 11.6344
A-Polynomial See Data:K11n99/A-polynomial

[edit Notes for K11n99's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11n99's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 39, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n99/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n99/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {10_144,}

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

Vassiliev invariants

V2 and V3: (-2, 6)
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 K11n99. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-8-7-6-5-4-3-2-10χ
-1        33
-3       21-1
-5      42 2
-7     32  -1
-9    34   -1
-11   33    0
-13  13     -2
-15 13      2
-17 1       -1
-191        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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K11n98.gif

K11n98

K11n100.gif

K11n100