L9a46

(Knotscape image)

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

Visit L9a46's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_12,6,13,5 X₈₄₉₃ X_2,14,3,13 X_14,7,15,8 X_16,12,17,11 X_18,9,11,10 X_10,17,5,18 X_4,15,1,16
Gauss code	{1, -4, 3, -9}, {2, -1, 5, -3, 7, -8}, {6, -2, 4, -5, 9, -6, 8, -7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 2 -2 v u 2 - v 2 w u 2 + 2 v w u 2 - w u 2 + u 2 -2 v 2 u + 4 v u + 2 v 2 w u -4 v w u + 2 w u -2 u + v 2 -2 v - v 2 w + 2 v w - w + 1$ (db)
Jones polynomial	$q 4 -4 q 3 + 7 q 2 -9 q + 12-10 q -1 + 10 q -2 -6 q -3 + 4 q -4 - q -5$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 6 + 2 a 2 z 4 + z 4 a -2 -3 z 4 - a 4 z 2 + 3 a 2 z 2 + z 2 a -2 -3 z 2 - a 2 + 1 + a 4 z -2 -2 a 2 z -2 + z -2$ (db)
Kauffman polynomial	$2 a 2 z 8 + 2 z 8 + 5 a 3 z 7 + 11 a z 7 + 6 z 7 a -1 + 4 a 4 z 6 + 8 a 2 z 6 + 7 z 6 a -2 + 11 z 6 + a 5 z 5 -8 a 3 z 5 -17 a z 5 -4 z 5 a -1 + 4 z 5 a -3 -8 a 4 z 4 -23 a 2 z 4 -9 z 4 a -2 + z 4 a -4 -25 z 4 - a 5 z 3 + 2 a 3 z 3 + 4 a z 3 -2 z 3 a -1 -3 z 3 a -3 + 4 a 4 z 2 + 12 a 2 z 2 + 4 z 2 a -2 + 12 z 2 - a 3 z - a z + a 4 + a 2 + 1 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 =

0 is the signature of L9a46. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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