L9n25

(Knotscape image)

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

Visit L9n25's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_5,12,6,13 X₈₄₉₃ X_2,14,3,13 X_14,7,15,8 X_11,16,12,17 X_9,11,10,18 X_17,5,18,10 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 $u$ , $v$ , $w$ , ...)	$v u - v w u + w u - u - v + v w - w + 1$ (db)
Jones polynomial	$q 2 - q + 4-2 q -1 + 3 q -2 -2 q -3 + 2 q -4 - q -5$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 2 a 4 - a 4 + z 4 a 2 + 3 z 2 a 2 + a 2 z -2 + 3 a 2 -2 z 2 -2 z -2 -3 + a -2 z -2 + a -2$ (db)
Kauffman polynomial	$a 3 z 7 + a z 7 + 2 a 4 z 6 + 3 a 2 z 6 + z 6 + a 5 z 5 -2 a 3 z 5 -3 a z 5 -7 a 4 z 4 -11 a 2 z 4 -4 z 4 -3 a 5 z 3 -2 a 3 z 3 + 2 a z 3 + z 3 a -1 + 5 a 4 z 2 + 13 a 2 z 2 + z 2 a -2 + 9 z 2 + a 5 z + 3 a 3 z + 3 a z + z a -1 -2 a 4 -6 a 2 -2 a -2 -5-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 L9n25. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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