L11n94

(Knotscape image)

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

Visit L11n94's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_12,4,13,3 X_9,14,10,15 X_19,22,20,5 X_11,21,12,20 X_21,11,22,10 X_15,19,16,18 X_7,17,8,16 X_17,9,18,8 X₂₅₃₆ X_4,14,1,13
Gauss code	{1, -10, 2, -11}, {10, -1, -8, 9, -3, 6, -5, -2, 11, 3, -7, 8, -9, 7, -4, 5, -6, 4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 3 + u 3 + v u 2 - u 2 - v u + u + v -1$ (db)
Jones polynomial	$q^{15/2}-q^{13/2}+q^{9/2}-2 q^{7/2}+2 q^{5/2}-4 q^{3/2}+3 \sqrt{q}-\frac{3}{\sqrt{q}}+\frac{2}{q^{3/2}}-\frac{1}{q^{5/2}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$- z 5 a -1 + a z 3 -4 z 3 a -1 + 2 z 3 a -3 - z 3 a -5 + 2 a z -5 z a -1 + 6 z a -3 -4 z a -5 + z a -7 + a z -1 -2 a -1 z -1 + 3 a -3 z -1 -3 a -5 z -1 + a -7 z -1$ (db)
Kauffman polynomial	$- z 9 a -1 - z 9 a -3 -4 z 8 a -2 -2 z 8 a -4 -2 z 8 - a z 7 + 2 z 7 a -1 + 3 z 7 a -3 - z 7 a -5 - z 7 a -7 + 21 z 6 a -2 + 12 z 6 a -4 - z 6 a -8 + 10 z 6 + 5 a z 5 + 9 z 5 a -1 + 6 z 5 a -3 + 8 z 5 a -5 + 6 z 5 a -7 -29 z 4 a -2 -18 z 4 a -4 + 3 z 4 a -6 + 5 z 4 a -8 -13 z 4 -7 a z 3 -19 z 3 a -1 -18 z 3 a -3 -14 z 3 a -5 -8 z 3 a -7 + 13 z 2 a -2 + 8 z 2 a -4 -5 z 2 a -6 -5 z 2 a -8 + 5 z 2 + 4 a z + 11 z a -1 + 14 z a -3 + 10 z a -5 + 3 z a -7 -2 a -2 + 2 a -6 + a -8 - a z -1 -2 a -1 z -1 -3 a -3 z -1 -3 a -5 z -1 - a -7 z -1$ (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 =

3 is the signature of L11n94. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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