K11a17

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K11a16.gif

K11a16

K11a18.gif

K11a18

K11a17.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a17 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8493 X12,6,13,5 X2837 X16,9,17,10 X6,12,7,11 X20,14,21,13 X10,15,11,16 X22,17,1,18 X14,20,15,19 X18,21,19,22
Gauss code 1, -4, 2, -1, 3, -6, 4, -2, 5, -8, 6, -3, 7, -10, 8, -5, 9, -11, 10, -7, 11, -9
Dowker-Thistlethwaite code 4 8 12 2 16 6 20 10 22 14 18
A Braid Representative
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A Morse Link Presentation K11a17 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:K11a17/ThurstonBennequinNumber
Hyperbolic Volume 16.1013
A-Polynomial See Data:K11a17/A-polynomial

[edit Notes for K11a17's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a17's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 123, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a17/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a17/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, 2)
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 K11a17. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-4-3-2-101234567χ
17           1-1
15          2 2
13         51 -4
11        82  6
9       95   -4
7      118    3
5     99     0
3    811      -3
1   610       4
-1  27        -5
-3 16         5
-5 2          -2
-71           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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K11a16.gif

K11a16

K11a18.gif

K11a18