L11a426

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,4,13,3 X_14,5,15,6 X_20,11,21,12 X_22,17,11,18 X_16,21,17,22 X_10,13,5,14 X_8,20,9,19 X_18,8,19,7 X_2,9,3,10 X_4,16,1,15
Gauss code	{1, -10, 2, -11}, {3, -1, 9, -8, 10, -7}, {4, -2, 7, -3, 11, -6, 5, -9, 8, -4, 6, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 4 - v u 4 - v 2 w u 4 + v w u 4 -3 v 2 u 3 + 6 v u 3 + 3 v 2 w u 3 -5 v w u 3 + w u 3 -2 u 3 + 3 v 2 u 2 -8 v u 2 -4 v 2 w u 2 + 8 v w u 2 -3 w u 2 + 4 u 2 - v 2 u + 5 v u + 2 v 2 w u -6 v w u + 3 w u -3 u - v + v w - w + 1$ (db)
Jones polynomial	$q 3 -4 q 2 + 10 q -15 + 23 q -1 -24 q -2 + 26 q -3 -22 q -4 + 16 q -5 -10 q -6 + 4 q -7 - q -8$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$- a 2 z 8 + 2 a 4 z 6 -5 a 2 z 6 + z 6 - a 6 z 4 + 7 a 4 z 4 -11 a 2 z 4 + 3 z 4 -2 a 6 z 2 + 10 a 4 z 2 -13 a 2 z 2 + 4 z 2 -2 a 6 + 8 a 4 -10 a 2 + 4- a 6 z -2 + 4 a 4 z -2 -5 a 2 z -2 + 2 z -2$ (db)
Kauffman polynomial	$2 a 4 z 10 + 2 a 2 z 10 + 7 a 5 z 9 + 14 a 3 z 9 + 7 a z 9 + 11 a 6 z 8 + 22 a 4 z 8 + 19 a 2 z 8 + 8 z 8 + 9 a 7 z 7 + 7 a 5 z 7 -13 a 3 z 7 -7 a z 7 + 4 z 7 a -1 + 4 a 8 z 6 -15 a 6 z 6 -56 a 4 z 6 -57 a 2 z 6 + z 6 a -2 -19 z 6 + a 9 z 5 -14 a 7 z 5 -37 a 5 z 5 -23 a 3 z 5 -9 a z 5 -8 z 5 a -1 -4 a 8 z 4 + 9 a 6 z 4 + 51 a 4 z 4 + 58 a 2 z 4 -2 z 4 a -2 + 18 z 4 - a 9 z 3 + 11 a 7 z 3 + 38 a 5 z 3 + 36 a 3 z 3 + 14 a z 3 + 4 z 3 a -1 + a 8 z 2 -5 a 6 z 2 -28 a 4 z 2 -35 a 2 z 2 + z 2 a -2 -12 z 2 -5 a 7 z -18 a 5 z -24 a 3 z -11 a z + 3 a 6 + 12 a 4 + 15 a 2 + 7 + a 7 z -1 + 5 a 5 z -1 + 9 a 3 z -1 + 5 a z -1 - a 6 z -2 -4 a 4 z -2 -5 a 2 z -2 -2 z -2$ (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 L11a426. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -3$	$i = -1$
$r = -7$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -4$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = -3$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -2$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{14}$
$r = -1$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = 0$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{14}$
$r = 1$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{7}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$