L8a14

(Knotscape image)

See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L8a14's page at the original Knot Atlas.

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

Planar diagram presentation	X_10,1,11,2 X_2,11,3,12 X_12,3,13,4 X_14,5,15,6 X_16,7,9,8 X_8,9,1,10 X_4,13,5,14 X_6,15,7,16
Gauss code	{1, -2, 3, -7, 4, -8, 5, -6}, {6, -1, 2, -3, 7, -4, 8, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- u 3 v 3 - u 2 v 2 - u v -1$ (db)
Jones polynomial	$-\frac{1}{q^{7/2}}-\frac{1}{q^{11/2}}+\frac{1}{q^{13/2}}-\frac{1}{q^{15/2}}+\frac{1}{q^{17/2}}-\frac{1}{q^{19/2}}+\frac{1}{q^{21/2}}-\frac{1}{q^{23/2}}$ (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)

The coefficients of the monomials

t r q j

are shown, along with their alternating sums

χ

(fixed

j

, alternation over

r

). The squares with yellow highlighting are those on the "critical diagonals", where

j -2 r = s + 1

j -2 r = s -1

, where

s =

-7 is the signature of L8a14. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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