L11a434

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 3 -2 v u 3 - v 2 w u 3 + 2 v w u 3 - w u 3 + u 3 + v 3 u 2 -5 v 2 u 2 + 6 v u 2 - v 3 w u 2 + 5 v 2 w u 2 -6 v w u 2 + 2 w u 2 -2 u 2 -2 v 3 u + 6 v 2 u -5 v u + 2 v 3 w u -6 v 2 w u + 5 v w u - w u + u + v 3 -2 v 2 + v - v 3 w + 2 v 2 w - v w$ (db)
Jones polynomial	$q 6 -4 q 5 + 8 q 4 -14 q 3 + 21 q 2 -22 q + 24-20 q -1 + 16 q -2 -9 q -3 + 4 q -4 - q -5$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 6 a -2 - z 6 + 2 a 2 z 4 -2 z 4 a -2 + z 4 a -4 - a 4 z 2 + a 2 z 2 -3 z 2 a -2 + z 2 a -4 + 2 z 2 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$2 z 10 a -2 + 2 z 10 + 7 a z 9 + 13 z 9 a -1 + 6 z 9 a -3 + 10 a 2 z 8 + 14 z 8 a -2 + 7 z 8 a -4 + 17 z 8 + 8 a 3 z 7 - a z 7 -20 z 7 a -1 -7 z 7 a -3 + 4 z 7 a -5 + 4 a 4 z 6 -14 a 2 z 6 -46 z 6 a -2 -18 z 6 a -4 + z 6 a -6 -45 z 6 + a 5 z 5 -11 a 3 z 5 -12 a z 5 + 3 z 5 a -1 -7 z 5 a -3 -10 z 5 a -5 -5 a 4 z 4 + 8 a 2 z 4 + 48 z 4 a -2 + 16 z 4 a -4 -2 z 4 a -6 + 43 z 4 - a 5 z 3 + 5 a 3 z 3 + 7 a z 3 + 5 z 3 a -1 + 10 z 3 a -3 + 6 z 3 a -5 + 2 a 4 z 2 -4 a 2 z 2 -20 z 2 a -2 -6 z 2 a -4 -20 z 2 + 1-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 L11a434. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -5$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -2$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = -1$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 0$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{14}$
$r = 1$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 2$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = 3$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 5$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 6$	${\mathbb Z}_2$	${\mathbb Z}$