L11n96

(Knotscape image)

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

Visit L11n96's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_12,3,13,4 X_7,16,8,17 X_9,18,10,19 X_17,8,18,9 X_22,20,5,19 X_20,14,21,13 X_14,22,15,21 X_15,10,16,11 X₂₅₃₆ X_4,11,1,12
Gauss code	{1, -10, 2, -11}, {10, -1, -3, 5, -4, 9, 11, -2, 7, -8, -9, 3, -5, 4, 6, -7, 8, -6}

A Braid Representative

A Morse Link Presentation

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

-3 is the signature of L11n96. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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