L11a364

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 4 u 4 + v 3 u 4 + v 4 u 3 -3 v 3 u 3 + 2 v 2 u 3 + 2 v 3 u 2 -3 v 2 u 2 + 2 v u 2 + 2 v 2 u -3 v u + u + v -1$ (db)
Jones polynomial	$q^{17/2}-2 q^{15/2}+3 q^{13/2}-5 q^{11/2}+6 q^{9/2}-7 q^{7/2}+6 q^{5/2}-6 q^{3/2}+4 \sqrt{q}-\frac{3}{\sqrt{q}}+\frac{2}{q^{3/2}}-\frac{1}{q^{5/2}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$- z 9 a -3 + z 7 a -1 -8 z 7 a -3 + z 7 a -5 + 6 z 5 a -1 -23 z 5 a -3 + 6 z 5 a -5 + 11 z 3 a -1 -28 z 3 a -3 + 11 z 3 a -5 + 7 z a -1 -12 z a -3 + 6 z a -5 + a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$- z 10 a -2 - z 10 a -4 -2 z 9 a -1 -4 z 9 a -3 -2 z 9 a -5 + 3 z 8 a -2 + 3 z 8 a -4 -2 z 8 a -6 -2 z 8 - a z 7 + 10 z 7 a -1 + 22 z 7 a -3 + 9 z 7 a -5 -2 z 7 a -7 + z 6 a -2 - z 6 a -4 + 6 z 6 a -6 -2 z 6 a -8 + 10 z 6 + 5 a z 5 -16 z 5 a -1 -45 z 5 a -3 -18 z 5 a -5 + 4 z 5 a -7 -2 z 5 a -9 -6 z 4 a -2 -5 z 4 a -4 -8 z 4 a -6 + 3 z 4 a -8 - z 4 a -10 -13 z 4 -6 a z 3 + 14 z 3 a -1 + 43 z 3 a -3 + 15 z 3 a -5 -4 z 3 a -7 + 4 z 3 a -9 + 5 z 2 a -2 + 5 z 2 a -4 + z 2 a -6 - z 2 a -8 + 2 z 2 a -10 + 4 z 2 + a z -7 z a -1 -14 z a -3 -5 z a -5 - z a -9 - a -2 + a -1 z -1 + a -3 z -1$ (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 =

3 is the signature of L11a364. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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