L10n95

(Knotscape image)

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Planar diagram presentation	X₈₁₉₂ X_18,12,19,11 X_3,10,4,11 X_19,2,20,3 X_16,8,17,7 X_9,13,10,20 X_12,18,7,17 X_4,13,5,14 X_14,5,15,6 X_6,15,1,16
Gauss code	{1, 4, -3, -8, 9, -10}, {5, -1, -6, 3, 2, -7}, {8, -9, 10, -5, 7, -2, -4, 6}

A Braid Representative

A Morse Link Presentation

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

-2 is the signature of L10n95. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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