L9a35

(Knotscape image)

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

Visit L9a35's page at the original Knot Atlas.

Planar diagram presentation	X_10,1,11,2 X_12,3,13,4 X_16,8,17,7 X_14,6,15,5 X_18,13,9,14 X_6,16,7,15 X_4,18,5,17 X_2,9,3,10 X_8,11,1,12
Gauss code	{1, -8, 2, -7, 4, -6, 3, -9}, {8, -1, 9, -2, 5, -4, 6, -3, 7, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 3 + v u 3 - v 3 u 2 + 3 v 2 u 2 -3 v u 2 + u 2 + v 3 u -3 v 2 u + 3 v u - u + v 2 - v$ (db)
Jones polynomial	$-q^{9/2}+3 q^{7/2}-5 q^{5/2}+6 q^{3/2}-7 \sqrt{q}+\frac{6}{\sqrt{q}}-\frac{6}{q^{3/2}}+\frac{3}{q^{5/2}}-\frac{2}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$a z 5 + z 5 a -1 - a 3 z 3 + 3 a z 3 + 2 z 3 a -1 - z 3 a -3 -2 a 3 z + 3 a z - z a -3 + a z -1 - a -1 z -1$ (db)
Kauffman polynomial	$- a 2 z 8 - z 8 -2 a 3 z 7 -5 a z 7 -3 z 7 a -1 - a 4 z 6 -5 z 6 a -2 -4 z 6 + 8 a 3 z 5 + 14 a z 5 + z 5 a -1 -5 z 5 a -3 + 4 a 4 z 4 + 7 a 2 z 4 + 6 z 4 a -2 -3 z 4 a -4 + 12 z 4 -10 a 3 z 3 -12 a z 3 + 4 z 3 a -1 + 5 z 3 a -3 - z 3 a -5 -4 a 4 z 2 -6 a 2 z 2 -2 z 2 a -2 + z 2 a -4 -5 z 2 + 4 a 3 z + 6 a z -2 z a -3 + 1- a z -1 - a -1 z -1$ (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 L9a35. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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