K11n113

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K11n112.gif

K11n112

K11n114.gif

K11n114

K11n113.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n113 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X10,3,11,4 X5,14,6,15 X18,7,19,8 X16,9,17,10 X2,11,3,12 X20,13,21,14 X15,22,16,1 X8,17,9,18 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
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A Morse Link Presentation K11n113 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:K11n113/ThurstonBennequinNumber
Hyperbolic Volume 11.0164
A-Polynomial See Data:K11n113/A-polynomial

[edit Notes for K11n113's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11n113's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 35, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n113/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n113/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (5, -12)
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 K11n113. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-9-8-7-6-5-4-3-2-10χ
-1         11
-3        21-1
-5       2  2
-7      32  -1
-9     32   1
-11    23    1
-13   33     0
-15  12      1
-17 13       -2
-19 1        1
-211         -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.

K11n112.gif

K11n112

K11n114.gif

K11n114