L11n205

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_7,16,8,17 X_18,12,19,11 X_2,19,3,20 X_3,12,4,13 X_13,21,14,20 X_14,5,15,6 X_6,9,7,10 X_22,16,9,15 X_17,8,18,1 X_21,4,22,5
Gauss code	{1, -4, -5, 11, 7, -8, -2, 10}, {8, -1, 3, 5, -6, -7, 9, 2, -10, -3, 4, 6, -11, -9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 5 - u 3 - v 3 u 2 - v 2$ (db)
Jones polynomial	$-\frac{1}{q^{7/2}}-\frac{1}{q^{17/2}}$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$z 3 a 7 + 4 z a 7 + 2 a 7 z -1 - z 5 a 5 -6 z 3 a 5 -9 z a 5 -3 a 5 z -1 + z a 3 + a 3 z -1$ (db)
Kauffman polynomial	$- z 7 a 9 + 7 z 5 a 9 -14 z 3 a 9 + 7 z a 9 + z 3 a 7 -4 z a 7 + 2 a 7 z -1 + z 6 a 6 -6 z 4 a 6 + 9 z 2 a 6 -3 a 6 + z 7 a 5 -7 z 5 a 5 + 15 z 3 a 5 -12 z a 5 + 3 a 5 z -1 + z 6 a 4 -6 z 4 a 4 + 9 z 2 a 4 -3 a 4 - z a 3 + a 3 z -1 - a 2$ (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 =

-2 is the signature of L11n205. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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