K11a327

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K11a326.gif

K11a326

K11a328.gif

K11a328

K11a327.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X6271 X12,4,13,3 X18,6,19,5 X16,7,17,8 X14,10,15,9 X4,12,5,11 X20,14,21,13 X22,15,1,16 X2,18,3,17 X10,20,11,19 X8,21,9,22
Gauss code 1, -9, 2, -6, 3, -1, 4, -11, 5, -10, 6, -2, 7, -5, 8, -4, 9, -3, 10, -7, 11, -8
Dowker-Thistlethwaite code 6 12 18 16 14 4 20 22 2 10 8
A Braid Representative
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A Morse Link Presentation K11a327 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11a327/ThurstonBennequinNumber
Hyperbolic Volume 19.2356
A-Polynomial See Data:K11a327/A-polynomial

[edit Notes for K11a327's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a327's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 187, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a327/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a327/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (3, 5)
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 K11a327. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-3-2-1012345678χ
19           11
17          4 -4
15         71 6
13        124  -8
11       147   7
9      1612    -4
7     1514     1
5    1116      5
3   915       -6
1  412        8
-1 18         -7
-3 4          4
-51           -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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K11a326.gif

K11a326

K11a328.gif

K11a328