L11a146

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 6 + v u 6 + 2 v 2 u 5 -3 v u 5 + u 5 -2 v 2 u 4 + 5 v u 4 -2 u 4 + 2 v 2 u 3 -5 v u 3 + 2 u 3 -2 v 2 u 2 + 5 v u 2 -2 u 2 + v 2 u -3 v u + 2 u + v -1$ (db)
Jones polynomial	$-q^{13/2}+3 q^{11/2}-5 q^{9/2}+9 q^{7/2}-12 q^{5/2}+13 q^{3/2}-14 \sqrt{q}+\frac{11}{\sqrt{q}}-\frac{9}{q^{3/2}}+\frac{5}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$z 9 a -1 - a z 7 + 7 z 7 a -1 - z 7 a -3 -5 a z 5 + 17 z 5 a -1 -5 z 5 a -3 -7 a z 3 + 15 z 3 a -1 -7 z 3 a -3 - a z + z a -1 - z a -3 + 2 a z -1 -3 a -1 z -1 + a -3 z -1$ (db)
Kauffman polynomial	$-2 z 10 a -2 -2 z 10 -4 a z 9 -8 z 9 a -1 -4 z 9 a -3 -4 a 2 z 8 + 3 z 8 a -2 -4 z 8 a -4 + 3 z 8 -3 a 3 z 7 + 13 a z 7 + 32 z 7 a -1 + 12 z 7 a -3 -4 z 7 a -5 - a 4 z 6 + 12 a 2 z 6 + 7 z 6 a -4 -3 z 6 a -6 + 3 z 6 + 10 a 3 z 5 -14 a z 5 -53 z 5 a -1 -20 z 5 a -3 + 8 z 5 a -5 - z 5 a -7 + 3 a 4 z 4 -7 a 2 z 4 -7 z 4 a -2 -2 z 4 a -4 + 7 z 4 a -6 -8 z 4 -7 a 3 z 3 + 6 a z 3 + 31 z 3 a -1 + 13 z 3 a -3 -3 z 3 a -5 + 2 z 3 a -7 - a 4 z 2 -3 z 2 a -4 -3 z 2 a -6 + z 2 + a 3 z + 2 a z - z a -1 -2 z a -3 + 3 a -2 + a -4 + 3-2 a z -1 -3 a -1 z -1 - a -3 z -1$ (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 L11a146. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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