K11a55

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K11a54.gif

K11a54

K11a56.gif

K11a56

K11a55.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a55 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8493 X16,6,17,5 X2837 X18,9,19,10 X20,11,21,12 X22,13,1,14 X6,16,7,15 X14,17,15,18 X10,19,11,20 X12,21,13,22
Gauss code 1, -4, 2, -1, 3, -8, 4, -2, 5, -10, 6, -11, 7, -9, 8, -3, 9, -5, 10, -6, 11, -7
Dowker-Thistlethwaite code 4 8 16 2 18 20 22 6 14 10 12
A Braid Representative {{{braid_table}}}
A Morse Link Presentation K11a55 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 4
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11a55/ThurstonBennequinNumber
Hyperbolic Volume 11.6846
A-Polynomial See Data:K11a55/A-polynomial

[edit Notes for K11a55's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a55's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 71, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (2, 1)
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 K11a55. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-6-5-4-3-2-1012345χ
9           1-1
7          1 1
5         31 -2
3        41  3
1       43   -1
-1      74    3
-3     55     0
-5    56      -1
-7   35       2
-9  25        -3
-11 13         2
-13 2          -2
-151           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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K11a54.gif

K11a54

K11a56.gif

K11a56