L11n206

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_16,8,17,7 X_18,12,19,11 X_19,3,20,2 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_8,18,1,17 X_4,22,5,21
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 $u$ , $v$ , $w$ , ...)	$- v 3 u 3 + v 2 u 3 + v 3 u 2 -3 v 2 u 2 + 2 v u 2 + 2 v 2 u -3 v u + u + v -1$ (db)
Jones polynomial	$q^{15/2}-2 q^{13/2}+3 q^{11/2}-4 q^{9/2}+5 q^{7/2}-6 q^{5/2}+4 q^{3/2}-4 \sqrt{q}+\frac{2}{\sqrt{q}}-\frac{1}{q^{3/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 7 a -3 + z 5 a -1 -6 z 5 a -3 + z 5 a -5 + 4 z 3 a -1 -12 z 3 a -3 + 4 z 3 a -5 + 5 z a -1 -9 z a -3 + 4 z a -5 + 2 a -1 z -1 -3 a -3 z -1 + a -5 z -1$ (db)
Kauffman polynomial	$- z 9 a -3 - z 9 a -5 - z 8 a -2 -3 z 8 a -4 -2 z 8 a -6 + 5 z 7 a -3 + 3 z 7 a -5 -2 z 7 a -7 + 4 z 6 a -2 + 13 z 6 a -4 + 8 z 6 a -6 - z 6 a -8 -3 z 5 a -1 -14 z 5 a -3 -3 z 5 a -5 + 8 z 5 a -7 -10 z 4 a -2 -21 z 4 a -4 -9 z 4 a -6 + 4 z 4 a -8 -2 z 4 - a z 3 + 5 z 3 a -1 + 18 z 3 a -3 + 5 z 3 a -5 -7 z 3 a -7 + 8 z 2 a -2 + 14 z 2 a -4 + 5 z 2 a -6 -3 z 2 a -8 + 2 z 2 + a z -5 z a -1 -11 z a -3 -4 z a -5 + z a -7 -3 a -2 -3 a -4 - a -6 + 2 a -1 z -1 + 3 a -3 z -1 + a -5 z -1$ (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 =

1 is the signature of L11n206. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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