L11a360

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 4 u 4 + v 3 u 4 + v 4 u 3 - v 3 u 3 + v 2 u 3 + v 3 u 2 - v 2 u 2 + v u 2 + v 2 u - v u + u + v -1$ (db)
Jones polynomial	$q 25 / 2 -2 q 23 / 2 + 2 q 21 / 2 -3 q 19 / 2 + 3 q 17 / 2 -3 q 15 / 2 + 3 q 13 / 2 -3 q 11 / 2 + 2 q 9 / 2 -2 q 7 / 2 + q 5 / 2 - q 3 / 2$ (db)
Signature	7 (db)
HOMFLY-PT polynomial	$- z 9 a -7 + z 7 a -5 -8 z 7 a -7 + z 7 a -9 + 7 z 5 a -5 -22 z 5 a -7 + 6 z 5 a -9 + 15 z 3 a -5 -25 z 3 a -7 + 10 z 3 a -9 + 10 z a -5 -11 z a -7 + 4 z a -9 + a -5 z -1 - a -7 z -1$ (db)
Kauffman polynomial	$- z 10 a -6 - z 10 a -8 - z 9 a -5 -3 z 9 a -7 -2 z 9 a -9 + 7 z 8 a -6 + 5 z 8 a -8 -2 z 8 a -10 + 8 z 7 a -5 + 21 z 7 a -7 + 11 z 7 a -9 -2 z 7 a -11 -15 z 6 a -6 -5 z 6 a -8 + 8 z 6 a -10 -2 z 6 a -12 -22 z 5 a -5 -48 z 5 a -7 -18 z 5 a -9 + 6 z 5 a -11 -2 z 5 a -13 + 9 z 4 a -6 -3 z 4 a -8 -6 z 4 a -10 + 4 z 4 a -12 -2 z 4 a -14 + 25 z 3 a -5 + 42 z 3 a -7 + 11 z 3 a -9 -2 z 3 a -11 + 2 z 3 a -13 -2 z 3 a -15 + 2 z 2 a -6 + 3 z 2 a -8 - z 2 a -10 + z 2 a -14 - z 2 a -16 -11 z a -5 -13 z a -7 -3 z a -9 - z a -11 + z a -13 + z a -15 - a -6 + a -5 z -1 + a -7 z -1$ (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 L11a360. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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