L11a365

(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_16,5,17,6 X_6,11,7,12 X_18,8,19,7 X_22,18,11,17 X_20,10,21,9 X_8,20,9,19 X_10,22,1,21 X_4,15,5,16
Gauss code	{1, -2, 3, -11, 4, -5, 6, -9, 8, -10}, {5, -1, 2, -3, 11, -4, 7, -6, 9, -8, 10, -7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 4 u 4 + v 3 u 4 + v 4 u 3 -3 v 3 u 3 + 2 v 2 u 3 + 2 v 3 u 2 -5 v 2 u 2 + 2 v u 2 + 2 v 2 u -3 v u + u + v -1$ (db)
Jones polynomial	$q^{9/2}-2 q^{7/2}+3 q^{5/2}-5 q^{3/2}+6 \sqrt{q}-\frac{8}{\sqrt{q}}+\frac{7}{q^{3/2}}-\frac{7}{q^{5/2}}+\frac{5}{q^{7/2}}-\frac{3}{q^{9/2}}+\frac{2}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- a z 9 + a 3 z 7 -8 a z 7 + z 7 a -1 + 6 a 3 z 5 -23 a z 5 + 6 z 5 a -1 + 11 a 3 z 3 -28 a z 3 + 11 z 3 a -1 + 6 a 3 z -13 a z + 6 z a -1 + a 3 z -1 - a z -1$ (db)
Kauffman polynomial	$- a 2 z 10 - z 10 -2 a 3 z 9 -4 a z 9 -2 z 9 a -1 -2 a 4 z 8 + 3 a 2 z 8 -2 z 8 a -2 + 3 z 8 -2 a 5 z 7 + 9 a 3 z 7 + 22 a z 7 + 9 z 7 a -1 -2 z 7 a -3 -2 a 6 z 6 + 6 a 4 z 6 - a 2 z 6 + 7 z 6 a -2 - z 6 a -4 - z 6 - a 7 z 5 + 5 a 5 z 5 -18 a 3 z 5 -48 a z 5 -16 z 5 a -1 + 8 z 5 a -3 + 6 a 6 z 4 -6 a 4 z 4 -9 a 2 z 4 -5 z 4 a -2 + 4 z 4 a -4 -6 z 4 + 3 a 7 z 3 -2 a 5 z 3 + 14 a 3 z 3 + 42 a z 3 + 16 z 3 a -1 -7 z 3 a -3 -3 a 6 z 2 + a 4 z 2 + 6 a 2 z 2 + z 2 a -2 -3 z 2 a -4 + 6 z 2 - a 7 z -6 a 3 z -14 a z -6 z a -1 + z a -3 - a 2 + a 3 z -1 + a z -1$ (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 L11a365. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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