L11a433

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 3 -2 v u 3 - v 2 w u 3 + 2 v w u 3 - w u 3 + u 3 + v 3 u 2 -3 v 2 u 2 + 4 v u 2 - v 3 w u 2 + 3 v 2 w u 2 -4 v w u 2 + 2 w u 2 -2 u 2 -2 v 3 u + 4 v 2 u -3 v u + 2 v 3 w u -4 v 2 w u + 3 v w u - w u + u + v 3 -2 v 2 + v - v 3 w + 2 v 2 w - v w$ (db)
Jones polynomial	$q 4 -4 q 3 + 8 q 2 -12 q + 16-17 q -1 + 18 q -2 -14 q -3 + 11 q -4 -6 q -5 + 4 q -6 - q -7$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 2 a 6 + a 6 z -2 + 2 z 4 a 4 + 3 z 2 a 4 -2 a 4 z -2 - a 4 - z 6 a 2 -2 z 4 a 2 -2 z 2 a 2 + a 2 z -2 - z 6 -2 z 4 - z 2 + 1 + z 4 a -2 + z 2 a -2$ (db)
Kauffman polynomial	$2 a 4 z 10 + 2 a 2 z 10 + 5 a 5 z 9 + 11 a 3 z 9 + 6 a z 9 + 4 a 6 z 8 + 4 a 4 z 8 + 9 a 2 z 8 + 9 z 8 + a 7 z 7 -18 a 5 z 7 -34 a 3 z 7 -5 a z 7 + 10 z 7 a -1 -16 a 6 z 6 -35 a 4 z 6 -38 a 2 z 6 + 8 z 6 a -2 -11 z 6 -3 a 7 z 5 + 17 a 5 z 5 + 30 a 3 z 5 -6 a z 5 -12 z 5 a -1 + 4 z 5 a -3 + 17 a 6 z 4 + 45 a 4 z 4 + 39 a 2 z 4 -8 z 4 a -2 + z 4 a -4 + 2 z 4 + a 7 z 3 -5 a 5 z 3 -9 a 3 z 3 + 2 a z 3 + 3 z 3 a -1 -2 z 3 a -3 -3 a 6 z 2 -13 a 4 z 2 -14 a 2 z 2 + 2 z 2 a -2 -2 z 2 + 4 a 5 z + 4 a 3 z -3 a 6 -4 a 4 - a 2 + 1-2 a 5 z -1 -2 a 3 z -1 + a 6 z -2 + 2 a 4 z -2 + a 2 z -2$ (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 L11a433. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -7$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -4$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{5}$
$r = -3$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = -2$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = -1$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 0$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{9}$
$r = 1$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 2$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$