L9a10

(Knotscape image)

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

Visit L9a10's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_16,7,17,8 X_4,17,1,18 X_12,6,13,5 X_10,4,11,3 X_18,12,5,11 X_14,9,15,10 X_2,14,3,13 X_8,15,9,16
Gauss code	{1, -8, 5, -3}, {4, -1, 2, -9, 7, -5, 6, -4, 8, -7, 9, -2, 3, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 3 + 2 u 3 + 4 v u 2 -4 u 2 -4 v u + 4 u + 2 v -2$ (db)
Jones polynomial	$-q^{9/2}+3 q^{7/2}-6 q^{5/2}+7 q^{3/2}-8 \sqrt{q}+\frac{8}{\sqrt{q}}-\frac{7}{q^{3/2}}+\frac{4}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$a z 5 + z 5 a -1 - a 3 z 3 + 2 a z 3 + 2 z 3 a -1 - z 3 a -3 - a 3 z + 2 z a -1 - z a -3 + a 3 z -1 -2 a z -1 + 2 a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$-2 a 2 z 8 -2 z 8 -3 a 3 z 7 -8 a z 7 -5 z 7 a -1 - a 4 z 6 + 3 a 2 z 6 -7 z 6 a -2 -3 z 6 + 11 a 3 z 5 + 22 a z 5 + 5 z 5 a -1 -6 z 5 a -3 + 3 a 4 z 4 + 4 a 2 z 4 + 10 z 4 a -2 -3 z 4 a -4 + 14 z 4 -11 a 3 z 3 -13 a z 3 + 5 z 3 a -1 + 6 z 3 a -3 - z 3 a -5 -2 a 4 z 2 -4 a 2 z 2 -4 z 2 a -2 -6 z 2 + a 3 z -2 a z -6 z a -1 -3 z a -3 + 1 + a 3 z -1 + 2 a z -1 + 2 a -1 z -1 + a -3 z -1$ (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 L9a10. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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