L9n14

(Knotscape image)

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

Visit L9n14's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_11,17,12,16 X_3,10,4,11 X_15,3,16,2 X_5,13,6,12 X₆₇₁₈ X_14,10,15,9 X_18,14,7,13 X_17,4,18,5
Gauss code	{1, 4, -3, 9, -5, -6}, {6, -1, 7, 3, -2, 5, 8, -7, -4, 2, -9, -8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 2 + v u 2 - v u + v -1$ (db)
Jones polynomial	$q^{9/2}-q^{7/2}+q^{5/2}-2 q^{3/2}+\sqrt{q}-\frac{2}{\sqrt{q}}+\frac{1}{q^{3/2}}-\frac{1}{q^{5/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- z 5 a -1 + a z 3 -5 z 3 a -1 + z 3 a -3 + 3 a z -7 z a -1 + 3 z a -3 + 2 a z -1 -3 a -1 z -1 + a -3 z -1$ (db)
Kauffman polynomial	$- z 7 a -1 - z 7 a -3 -2 z 6 a -2 - z 6 a -4 - z 6 + 5 z 5 a -1 + 5 z 5 a -3 + 9 z 4 a -2 + 5 z 4 a -4 + 4 z 4 -2 a z 3 -9 z 3 a -1 -7 z 3 a -3 - a 2 z 2 -10 z 2 a -2 -6 z 2 a -4 -5 z 2 - a 3 z + 4 a z + 9 z a -1 + 4 z a -3 + 3 a -2 + a -4 + 3-2 a z -1 -3 a -1 z -1 - a -3 z -1$ (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 L9n14. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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