L11a484

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,7,15,8 X_4,15,1,16 X_12,6,13,5 X₈₄₉₃ X_16,10,17,9 X_22,17,19,18 X_20,12,21,11 X_10,20,11,19 X_18,21,5,22 X_2,14,3,13
Gauss code	{1, -11, 5, -3}, {9, -8, 10, -7}, {4, -1, 2, -5, 6, -9, 8, -4, 11, -2, 3, -6, 7, -10}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 5 - v w u 5 + w u 5 - u 5 -3 v u 4 + 3 v w u 4 -3 w u 4 + 3 u 4 + 4 v u 3 -4 v w u 3 + 4 w u 3 -4 u 3 -4 v u 2 + 4 v w u 2 -4 w u 2 + 4 u 2 + 3 v u -3 v w u + 3 w u -3 u - v + v w - w + 1$ (db)
Jones polynomial	$q 7 -4 q 6 + 8 q 5 -13 q 4 + 18 q 3 -20 q 2 + 21 q -16 + 14 q -1 -8 q -2 + 4 q -3 - q -4$ (db)
Signature	2 (db)
HOMFLY-PT polynomial	$- z 8 a -2 -5 z 6 a -2 + z 6 a -4 + 2 z 6 - a 2 z 4 -9 z 4 a -2 + 3 z 4 a -4 + 7 z 4 -2 a 2 z 2 -6 z 2 a -2 + 2 z 2 a -4 + 6 z 2 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$2 z 10 a -2 + 2 z 10 + 5 a z 9 + 13 z 9 a -1 + 8 z 9 a -3 + 4 a 2 z 8 + 18 z 8 a -2 + 12 z 8 a -4 + 10 z 8 + a 3 z 7 -12 a z 7 -30 z 7 a -1 -6 z 7 a -3 + 11 z 7 a -5 -14 a 2 z 6 -67 z 6 a -2 -20 z 6 a -4 + 8 z 6 a -6 -53 z 6 -3 a 3 z 5 - a z 5 + z 5 a -1 -18 z 5 a -3 -13 z 5 a -5 + 4 z 5 a -7 + 16 a 2 z 4 + 66 z 4 a -2 + 12 z 4 a -4 -7 z 4 a -6 + z 4 a -8 + 62 z 4 + 3 a 3 z 3 + 12 a z 3 + 23 z 3 a -1 + 20 z 3 a -3 + 4 z 3 a -5 -2 z 3 a -7 -8 a 2 z 2 -21 z 2 a -2 -5 z 2 a -4 + z 2 a -6 -23 z 2 - a 3 z -4 a z -6 z a -1 -4 z a -3 - z a -5 + 1-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 =

2 is the signature of L11a484. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 1$	$i = 3$
$r = -5$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -2$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -1$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 0$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{11}$
$r = 1$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 2$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 3$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 5$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 6$	${\mathbb Z}_2$	${\mathbb Z}$