K11a303

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K11a302.gif

K11a302

K11a304.gif

K11a304

K11a303.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a303 at Knotilus!



Knot presentations

Planar diagram presentation X6271 X10,3,11,4 X18,5,19,6 X22,8,1,7 X16,10,17,9 X4,11,5,12 X8,14,9,13 X20,16,21,15 X12,18,13,17 X2,19,3,20 X14,22,15,21
Gauss code 1, -10, 2, -6, 3, -1, 4, -7, 5, -2, 6, -9, 7, -11, 8, -5, 9, -3, 10, -8, 11, -4
Dowker-Thistlethwaite code 6 10 18 22 16 4 8 20 12 2 14
A Braid Representative
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A Morse Link Presentation K11a303 ML.gif

Three dimensional invariants

Symmetry type Chiral
Unknotting number
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11a303/ThurstonBennequinNumber
Hyperbolic Volume 17.779
A-Polynomial See Data:K11a303/A-polynomial

[edit Notes for K11a303's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant 0

[edit Notes for K11a303's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 149, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a303/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a303/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, 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 0 is the signature of K11a303. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-4-3-2-101234567χ
15           1-1
13          3 3
11         61 -5
9        93  6
7       116   -5
5      139    4
3     1111     0
1    1013      -3
-1   712       5
-3  39        -6
-5 17         6
-7 3          -3
-91           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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K11a302.gif

K11a302

K11a304.gif

K11a304