L11a441

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,3,15,4 X_12,15,5,16 X_22,17,13,18 X_16,7,17,8 X_8,22,9,21 X_20,12,21,11 X_18,10,19,9 X_10,20,11,19 X₂₅₃₆ X_4,13,1,14
Gauss code	{1, -10, 2, -11}, {10, -1, 5, -6, 8, -9, 7, -3}, {11, -2, 3, -5, 4, -8, 9, -7, 6, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 3 u 3 + 2 v 2 u 3 - v u 3 - v 2 w u 3 + v w u 3 + 2 v 3 u 2 -6 v 2 u 2 + 4 v u 2 - v 3 w u 2 + 4 v 2 w u 2 -4 v w u 2 + w u 2 - u 2 - v 3 u + 4 v 2 u -4 v u + v 3 w u -4 v 2 w u + 6 v w u -2 w u + u - v 2 + v + v 2 w -2 v w + w$ (db)
Jones polynomial	$q 4 -4 q 3 + 9 q 2 -13 q + 17-18 q -1 + 19 q -2 -14 q -3 + 11 q -4 -6 q -5 + 3 q -6 - q -7$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 2 a 6 -2 a 6 + 3 z 4 a 4 + 9 z 2 a 4 + a 4 z -2 + 7 a 4 -2 z 6 a 2 -8 z 4 a 2 -13 z 2 a 2 -2 a 2 z -2 -9 a 2 - z 6 - z 4 + 3 z 2 + z -2 + 4 + z 4 a -2 + z 2 a -2$ (db)
Kauffman polynomial	$a 4 z 10 + a 2 z 10 + 3 a 5 z 9 + 8 a 3 z 9 + 5 a z 9 + 3 a 6 z 8 + 9 a 4 z 8 + 16 a 2 z 8 + 10 z 8 + a 7 z 7 -6 a 5 z 7 -13 a 3 z 7 + 6 a z 7 + 12 z 7 a -1 -12 a 6 z 6 -41 a 4 z 6 -48 a 2 z 6 + 9 z 6 a -2 -10 z 6 -4 a 7 z 5 -6 a 5 z 5 -11 a 3 z 5 -29 a z 5 -16 z 5 a -1 + 4 z 5 a -3 + 16 a 6 z 4 + 55 a 4 z 4 + 47 a 2 z 4 -9 z 4 a -2 + z 4 a -4 -2 z 4 + 5 a 7 z 3 + 17 a 5 z 3 + 24 a 3 z 3 + 20 a z 3 + 7 z 3 a -1 - z 3 a -3 -9 a 6 z 2 -34 a 4 z 2 -29 a 2 z 2 + 4 z 2 a -2 -2 a 7 z -7 a 5 z -12 a 3 z -8 a z - z a -1 + 3 a 6 + 11 a 4 + 11 a 2 - a -2 + 3 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 L11a441. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -7$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -4$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{5}$
$r = -3$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = -2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = -1$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 0$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{10}$
$r = 1$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 2$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$