L11a464

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,7,13,8 X_4,13,1,14 X_16,6,17,5 X₈₄₉₃ X_20,9,21,10 X_10,19,11,20 X_22,18,15,17 X_18,22,19,21 X_14,16,5,15 X_2,12,3,11
Gauss code	{1, -11, 5, -3}, {10, -4, 8, -9, 7, -6, 9, -8}, {4, -1, 2, -5, 6, -7, 11, -2, 3, -10}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u 3 -2 v w u 3 + 2 w u 3 -2 u 3 -6 v u 2 + 6 v w u 2 -6 w u 2 + 6 u 2 + 6 v u -6 v w u + 6 w u -6 u -2 v + 2 v w -2 w + 2$ (db)
Jones polynomial	$q 6 -5 q 5 + 10 q 4 -14 q 3 + 19 q 2 -20 q + 21-16 q -1 + 12 q -2 -6 q -3 + 3 q -4 - q -5$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 6 a -2 - z 6 + 2 a 2 z 4 - z 4 a -2 + z 4 a -4 -2 z 4 - a 4 z 2 + 4 a 2 z 2 + 2 z 2 a -2 -5 z 2 - a 4 + 4 a 2 + 4 a -2 - a -4 -6 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$2 z 10 a -2 + 2 z 10 + 4 a z 9 + 11 z 9 a -1 + 7 z 9 a -3 + 4 a 2 z 8 + 11 z 8 a -2 + 9 z 8 a -4 + 6 z 8 + 4 a 3 z 7 -20 z 7 a -1 -11 z 7 a -3 + 5 z 7 a -5 + 3 a 4 z 6 + 3 a 2 z 6 -33 z 6 a -2 -22 z 6 a -4 + z 6 a -6 -10 z 6 + a 5 z 5 -3 a 3 z 5 -3 a z 5 + 9 z 5 a -1 -2 z 5 a -3 -10 z 5 a -5 -6 a 4 z 4 -17 a 2 z 4 + 16 z 4 a -2 + 11 z 4 a -4 - z 4 a -6 -7 z 4 -2 a 5 z 3 -3 a 3 z 3 - a z 3 - z 3 a -1 + z 3 a -3 + 2 z 3 a -5 + 5 a 4 z 2 + 18 a 2 z 2 + 10 z 2 a -2 + z 2 a -4 + 22 z 2 + a 5 z + 3 a 3 z + 4 a z + 4 z a -1 + 3 z a -3 + z a -5 -2 a 4 -8 a 2 -8 a -2 -2 a -4 -11-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 =

0 is the signature of L11a464. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -5$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -2$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 0$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{12}$
$r = 1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 2$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 4$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 5$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 6$	${\mathbb Z}_2$	${\mathbb Z}$