L11a180

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_10,4,11,3 X_14,6,15,5 X_16,8,17,7 X_22,18,7,17 X_12,15,13,16 X_20,10,21,9 X_18,11,19,12 X_6,14,1,13 X_4,20,5,19 X_2,21,3,22
Gauss code	{1, -11, 2, -10, 3, -9}, {4, -1, 7, -2, 8, -6, 9, -3, 6, -4, 5, -8, 10, -7, 11, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + 2 v u 4 - u 4 + 5 v 2 u 3 -11 v u 3 + 6 u 3 -9 v 2 u 2 + 19 v u 2 -9 u 2 + 6 v 2 u -11 v u + 5 u - v 2 + 2 v -1$ (db)
Jones polynomial	$q^{15/2}-4 q^{13/2}+10 q^{11/2}-18 q^{9/2}+24 q^{7/2}-29 q^{5/2}+29 q^{3/2}-26 \sqrt{q}+\frac{19}{\sqrt{q}}-\frac{12}{q^{3/2}}+\frac{5}{q^{5/2}}-\frac{1}{q^{7/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 7 a -1 + a z 5 -3 z 5 a -1 + 3 z 5 a -3 + a z 3 -5 z 3 a -1 + 5 z 3 a -3 -3 z 3 a -5 + a z - z a -1 + 2 z a -3 -2 z a -5 + z a -7 + a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$-3 z 10 a -2 -3 z 10 a -4 -11 z 9 a -1 -19 z 9 a -3 -8 z 9 a -5 -27 z 8 a -2 -19 z 8 a -4 -8 z 8 a -6 -16 z 8 -12 a z 7 + 23 z 7 a -3 + 7 z 7 a -5 -4 z 7 a -7 -5 a 2 z 6 + 65 z 6 a -2 + 54 z 6 a -4 + 16 z 6 a -6 - z 6 a -8 + 23 z 6 - a 3 z 5 + 15 a z 5 + 26 z 5 a -1 + 12 z 5 a -3 + 10 z 5 a -5 + 8 z 5 a -7 + 3 a 2 z 4 -41 z 4 a -2 -41 z 4 a -4 -12 z 4 a -6 + 2 z 4 a -8 -11 z 4 -6 a z 3 -15 z 3 a -1 -15 z 3 a -3 -12 z 3 a -5 -6 z 3 a -7 + 8 z 2 a -2 + 10 z 2 a -4 + 4 z 2 a -6 - z 2 a -8 + 3 z 2 + a z + 3 z a -5 + 2 z a -7 - a -2 + a -1 z -1 + a -3 z -1$ (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 =

1 is the signature of L11a180. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 0$	$i = 2$
$r = -4$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -2$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 0$	${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{12}$
$r = 1$	${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{14}$	${\mathbb Z}^{14}$
$r = 2$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{15}$	${\mathbb Z}^{16}$
$r = 3$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = 4$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 5$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 6$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 7$	${\mathbb Z}_2$	${\mathbb Z}$