L11a332

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_2,11,3,12 X_12,3,13,4 X_20,5,21,6 X_22,13,9,14 X_18,21,19,22 X_16,7,17,8 X_14,17,15,18 X_8,9,1,10 X_6,15,7,16 X_4,19,5,20
Gauss code	{1, -2, 3, -11, 4, -10, 7, -9}, {9, -1, 2, -3, 5, -8, 10, -7, 8, -6, 11, -4, 6, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-3 v 3 u 3 + 3 v 2 u 3 - v u 3 + 3 v 3 u 2 -8 v 2 u 2 + 5 v u 2 - u 2 - v 3 u + 5 v 2 u -8 v u + 3 u - v 2 + 3 v -3$ (db)
Jones polynomial	$-\frac{1}{q^{7/2}}+\frac{2}{q^{9/2}}-\frac{6}{q^{11/2}}+\frac{8}{q^{13/2}}-\frac{12}{q^{15/2}}+\frac{15}{q^{17/2}}-\frac{15}{q^{19/2}}+\frac{14}{q^{21/2}}-\frac{11}{q^{23/2}}+\frac{7}{q^{25/2}}-\frac{4}{q^{27/2}}+\frac{1}{q^{29/2}}$ (db)
Signature	-7 (db)
HOMFLY-PT polynomial	$- z 3 a 13 -2 z a 13 + 3 z 5 a 11 + 11 z 3 a 11 + 9 z a 11 -2 z 7 a 9 -10 z 5 a 9 -15 z 3 a 9 -6 z a 9 + a 9 z -1 - z 7 a 7 -5 z 5 a 7 -8 z 3 a 7 -5 z a 7 - a 7 z -1$ (db)
Kauffman polynomial	$- z 4 a 18 -4 z 5 a 17 + 3 z 3 a 17 -7 z 6 a 16 + 7 z 4 a 16 - z 2 a 16 -8 z 7 a 15 + 8 z 5 a 15 + z 3 a 15 -2 z a 15 -7 z 8 a 14 + 8 z 6 a 14 - z 4 a 14 -4 z 9 a 13 + 12 z 5 a 13 -7 z 3 a 13 - z a 13 - z 10 a 12 -10 z 8 a 12 + 37 z 6 a 12 -42 z 4 a 12 + 18 z 2 a 12 -7 z 9 a 11 + 20 z 7 a 11 -18 z 5 a 11 + 12 z 3 a 11 -7 z a 11 - z 10 a 10 -5 z 8 a 10 + 29 z 6 a 10 -38 z 4 a 10 + 16 z 2 a 10 -3 z 9 a 9 + 11 z 7 a 9 -13 z 5 a 9 + 9 z 3 a 9 -3 z a 9 - a 9 z -1 -2 z 8 a 8 + 7 z 6 a 8 -5 z 4 a 8 - z 2 a 8 + a 8 - z 7 a 7 + 5 z 5 a 7 -8 z 3 a 7 + 5 z a 7 - a 7 z -1$ (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 L11a332. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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