L11n130

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_11,19,12,18 X_3,10,4,11 X_17,3,18,2 X_5,13,6,12 X₆₇₁₈ X_9,16,10,17 X_13,20,14,21 X_15,22,16,7 X_19,4,20,5 X_21,14,22,15
Gauss code	{1, 4, -3, 10, -5, -6}, {6, -1, -7, 3, -2, 5, -8, 11, -9, 7, -4, 2, -10, 8, -11, 9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + v u 4 + 2 v 2 u 3 -4 v u 3 + u 3 -2 v 2 u 2 + 5 v u 2 -2 u 2 + v 2 u -4 v u + 2 u + v -1$ (db)
Jones polynomial	$\frac{1}{\sqrt{q}}-\frac{4}{q^{3/2}}+\frac{5}{q^{5/2}}-\frac{9}{q^{7/2}}+\frac{9}{q^{9/2}}-\frac{9}{q^{11/2}}+\frac{8}{q^{13/2}}-\frac{5}{q^{15/2}}+\frac{3}{q^{17/2}}-\frac{1}{q^{19/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$z 5 a 7 + 3 z 3 a 7 + 2 z a 7 - a 7 z -1 - z 7 a 5 -5 z 5 a 5 -8 z 3 a 5 -2 z a 5 + 3 a 5 z -1 + z 5 a 3 + 2 z 3 a 3 - z a 3 -2 a 3 z -1$ (db)
Kauffman polynomial	$- z 5 a 11 + 2 z 3 a 11 -3 z 6 a 10 + 7 z 4 a 10 -3 z 2 a 10 -4 z 7 a 9 + 9 z 5 a 9 -5 z 3 a 9 + z a 9 -3 z 8 a 8 + 5 z 6 a 8 -2 z 4 a 8 - z 2 a 8 + a 8 - z 9 a 7 -2 z 7 a 7 + 5 z 5 a 7 -3 z 3 a 7 - a 7 z -1 -4 z 8 a 6 + 9 z 6 a 6 -12 z 4 a 6 + 3 z 2 a 6 + 3 a 6 - z 9 a 5 + 2 z 7 a 5 -9 z 5 a 5 + 10 z 3 a 5 - z a 5 -3 a 5 z -1 - z 8 a 4 + z 6 a 4 -4 z 4 a 4 + 2 z 2 a 4 + 3 a 4 -4 z 5 a 3 + 6 z 3 a 3 -2 a 3 z -1 - z 4 a 2 + z 2 a 2$ (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 =

-3 is the signature of L11n130. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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