# L8a14

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## Contents

 (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 on a church of Murato,Corsica

### 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}

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

### 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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