L8a14

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L8a13

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L8a15

Contents

L8a14.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L8a14 at Knotilus!

L8a14 is 8^2_{1} in the Rolfsen table of links.

Floor of the Stock Exchange [1]
Represented as two interlaced squares
A mosaic seen on an Istanbul floor
Coat of arms of Jaroměř, Czech Republic
Coat of arms of St. Savior, Jersey, Channel Islands, depicting Crown of Thorns religious symbol
Cathedral in Tbilisi, Georgia
Coat of arms of Mozota, Spain
Decorative motif of interlaced squares, San Pancrazio, Florence
Macedonian cross
3D depiction
Arma Christi carving in monastery in Portugal
Handewitt, Schleswig-Holstein oak leaves and acorns
Flower carpet, south India
Flower carpet, south India
Islamic art tile
moroccan craft

Link Presentations

[edit Notes on L8a14's Link Presentations]

Planar diagram presentation X10,1,11,2 X2,11,3,12 X12,3,13,4 X14,5,15,6 X16,7,9,8 X8,9,1,10 X4,13,5,14 X6,15,7,16
Gauss code {1, -2, 3, -7, 4, -8, 5, -6}, {6, -1, 2, -3, 7, -4, 8, -5}
A Braid Representative
BraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gif
BraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gif
A Morse Link Presentation L8a14 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{(u v+1) \left(u^2 v^2+1\right)}{u^{3/2} v^{3/2}} (db)
Jones polynomial -\frac{1}{q^{7/2}}-\frac{1}{q^{23/2}}+\frac{1}{q^{21/2}}-\frac{1}{q^{19/2}}+\frac{1}{q^{17/2}}-\frac{1}{q^{15/2}}+\frac{1}{q^{13/2}}-\frac{1}{q^{11/2}} (db)
Signature -7 (db)
HOMFLY-PT polynomial z^5 a^9+5 z^3 a^9+6 z a^9+a^9 z^{-1} -z^7 a^7-7 z^5 a^7-15 z^3 a^7-10 z a^7-a^7 z^{-1} (db)
Kauffman polynomial -z a^{15}-z^2 a^{14}-z^3 a^{13}+z a^{13}-z^4 a^{12}+2 z^2 a^{12}-z^5 a^{11}+3 z^3 a^{11}-z a^{11}-z^6 a^{10}+4 z^4 a^{10}-3 z^2 a^{10}-z^7 a^9+6 z^5 a^9-11 z^3 a^9+7 z a^9-a^9 z^{-1} -z^6 a^8+5 z^4 a^8-6 z^2 a^8+a^8-z^7 a^7+7 z^5 a^7-15 z^3 a^7+10 z a^7-a^7 z^{-1} (db)

Khovanov Homology

The coefficients of the monomials t^rq^j are shown, along with their alternating sums \chi (fixed j, alternation over r).   
\ r
  \  
j \
-8-7-6-5-4-3-2-10χ
-6        11
-8        11
-10      1  1
-12         0
-14    11   0
-16         0
-18  11     0
-20         0
-2211       0
-241        1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=-8 i=-6
r=-8 {\mathbb Z} {\mathbb Z}
r=-7 {\mathbb Z}
r=-6 {\mathbb Z}_2 {\mathbb Z}
r=-5 {\mathbb Z}
r=-4 {\mathbb Z}_2 {\mathbb Z}
r=-3 {\mathbb Z}
r=-2 {\mathbb Z}_2 {\mathbb Z}
r=-1
r=0 {\mathbb Z} {\mathbb Z}

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 Link Page master template (intermediate).

See/edit the Link_Splice_Base (expert).

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L8a13

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