K11a50

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K11a49.gif

K11a49

K11a51.gif

K11a51

K11a50.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X4251 X8394 X14,6,15,5 X10,8,11,7 X2,9,3,10 X18,12,19,11 X6,14,7,13 X22,16,1,15 X20,18,21,17 X12,20,13,19 X16,22,17,21
Gauss code 1, -5, 2, -1, 3, -7, 4, -2, 5, -4, 6, -10, 7, -3, 8, -11, 9, -6, 10, -9, 11, -8
Dowker-Thistlethwaite code 4 8 14 10 2 18 6 22 20 12 16
A Braid Representative
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A Morse Link Presentation K11a50 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:K11a50/ThurstonBennequinNumber
Hyperbolic Volume 13.4737
A-Polynomial See Data:K11a50/A-polynomial

[edit Notes for K11a50's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a50's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 83, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a50/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a50/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (1, 4)
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 K11a50. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-2-10123456789χ
21           1-1
19          2 2
17         41 -3
15        52  3
13       64   -2
11      75    2
9     66     0
7    57      -2
5   36       3
3  25        -3
1 14         3
-1 1          -1
-31           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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K11a49.gif

K11a49

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K11a51