L9a36

(Knotscape image)

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

Visit L9a36's page at the original Knot Atlas.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 3 u 3 + v 2 u 3 + v 3 u 2 - v 2 u 2 + v u 2 + v 2 u - v u + u + v -1$ (db)
Jones polynomial	$q^{19/2}-2 q^{17/2}+2 q^{15/2}-3 q^{13/2}+3 q^{11/2}-3 q^{9/2}+2 q^{7/2}-2 q^{5/2}+q^{3/2}-\sqrt{q}$ (db)
Signature	5 (db)
HOMFLY-PT polynomial	$- z 7 a -5 + z 5 a -3 -6 z 5 a -5 + z 5 a -7 + 5 z 3 a -3 -11 z 3 a -5 + 4 z 3 a -7 + 6 z a -3 -7 z a -5 + 3 z a -7 + a -3 z -1 - a -5 z -1$ (db)
Kauffman polynomial	$- z 8 a -4 - z 8 a -6 - z 7 a -3 -3 z 7 a -5 -2 z 7 a -7 + 5 z 6 a -4 + 3 z 6 a -6 -2 z 6 a -8 + 6 z 5 a -3 + 15 z 5 a -5 + 7 z 5 a -7 -2 z 5 a -9 -6 z 4 a -4 + 4 z 4 a -8 -2 z 4 a -10 -11 z 3 a -3 -21 z 3 a -5 -6 z 3 a -7 + 2 z 3 a -9 -2 z 3 a -11 -2 z 2 a -6 + z 2 a -10 - z 2 a -12 + 7 z a -3 + 9 z a -5 + 2 z a -7 + z a -9 + z a -11 + a -4 - a -3 z -1 - a -5 z -1$ (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 =

5 is the signature of L9a36. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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