L11a495

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_16,7,17,8 X_4,17,1,18 X_22,12,19,11 X_10,4,11,3 X_20,5,21,6 X_18,21,5,22 X_12,20,13,19 X_14,9,15,10 X_2,14,3,13 X_8,15,9,16
Gauss code	{1, -10, 5, -3}, {8, -6, 7, -4}, {6, -1, 2, -11, 9, -5, 4, -8, 10, -9, 11, -2, 3, -7}

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	$q 4 -4 q 3 + 10 q 2 -14 q + 19-20 q -1 + 21 q -2 -16 q -3 + 12 q -4 -7 q -5 + 3 q -6 - q -7$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 2 a 6 - a 6 + 2 z 4 a 4 + 3 z 2 a 4 + a 4 - z 6 a 2 - z 4 a 2 + z 2 a 2 + a 2 z -2 + 3 a 2 - z 6 -2 z 4 -4 z 2 -2 z -2 -5 + z 4 a -2 + z 2 a -2 + a -2 z -2 + 2 a -2$ (db)
Kauffman polynomial	$2 a 4 z 10 + 2 a 2 z 10 + 4 a 5 z 9 + 12 a 3 z 9 + 8 a z 9 + 3 a 6 z 8 + 5 a 4 z 8 + 15 a 2 z 8 + 13 z 8 + a 7 z 7 -11 a 5 z 7 -31 a 3 z 7 -5 a z 7 + 14 z 7 a -1 -11 a 6 z 6 -33 a 4 z 6 -48 a 2 z 6 + 10 z 6 a -2 -16 z 6 -4 a 7 z 5 + 5 a 5 z 5 + 21 a 3 z 5 -10 a z 5 -18 z 5 a -1 + 4 z 5 a -3 + 13 a 6 z 4 + 41 a 4 z 4 + 34 a 2 z 4 -10 z 4 a -2 + z 4 a -4 -5 z 4 + 5 a 7 z 3 + 5 a 5 z 3 -6 a 3 z 3 -2 a z 3 + 4 z 3 a -1 -7 a 6 z 2 -17 a 4 z 2 - a 2 z 2 + 6 z 2 a -2 + 15 z 2 -2 a 7 z -3 a 5 z + 3 a 3 z + 7 a z + 3 z a -1 + 2 a 6 + 2 a 4 -6 a 2 -4 a -2 -9-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 L11a495. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -7$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -4$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -3$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = -2$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = 0$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{12}$
$r = 1$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 2$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$