L11a35

(Knotscape image)

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

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Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_16,8,17,7 X_18,13,19,14 X_14,17,15,18 X_22,20,5,19 X_20,12,21,11 X_12,22,13,21 X_8,16,9,15 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -10, 2, -11}, {10, -1, 3, -9, 11, -2, 7, -8, 4, -5, 9, -3, 5, -4, 6, -7, 8, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- u 5 -2 v u 4 + 6 u 4 + 7 v u 3 -9 u 3 -9 v u 2 + 7 u 2 + 6 v u -2 u - v$ (db)
Jones polynomial	$q^{11/2}-3 q^{9/2}+6 q^{7/2}-10 q^{5/2}+14 q^{3/2}-16 \sqrt{q}+\frac{15}{\sqrt{q}}-\frac{14}{q^{3/2}}+\frac{10}{q^{5/2}}-\frac{7}{q^{7/2}}+\frac{3}{q^{9/2}}-\frac{1}{q^{11/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$z a 5 + a 5 z -1 -3 z 3 a 3 -5 z a 3 -2 a 3 z -1 + 2 z 5 a + 5 z 3 a + 6 z a + 3 a z -1 + z 5 a -1 - z 3 a -1 -4 z a -1 -3 a -1 z -1 -2 z 3 a -3 - z a -3 + a -3 z -1 + z a -5$ (db)
Kauffman polynomial	$- a 2 z 10 - z 10 -3 a 3 z 9 -7 a z 9 -4 z 9 a -1 -3 a 4 z 8 -8 a 2 z 8 -6 z 8 a -2 -11 z 8 - a 5 z 7 + 5 a 3 z 7 + 11 a z 7 - z 7 a -1 -6 z 7 a -3 + 11 a 4 z 6 + 36 a 2 z 6 + 5 z 6 a -2 -5 z 6 a -4 + 35 z 6 + 4 a 5 z 5 + 11 a 3 z 5 + 18 a z 5 + 19 z 5 a -1 + 5 z 5 a -3 -3 z 5 a -5 -12 a 4 z 4 -38 a 2 z 4 + 5 z 4 a -2 + 5 z 4 a -4 - z 4 a -6 -27 z 4 -6 a 5 z 3 -22 a 3 z 3 -35 a z 3 -23 z 3 a -1 - z 3 a -3 + 3 z 3 a -5 + 4 a 4 z 2 + 14 a 2 z 2 -8 z 2 a -2 -3 z 2 a -4 + z 2 a -6 + 6 z 2 + 4 a 5 z + 11 a 3 z + 18 a z + 13 z a -1 + z a -3 - z a -5 -2 a 2 + 2 a -2 + a -4 - a 5 z -1 -2 a 3 z -1 -3 a z -1 -3 a -1 z -1 - a -3 z -1$ (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 L11a35. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 0$	$i = 2$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{3}$
$r = -3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -2$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = -1$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 0$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{8}$
$r = 1$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 3$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$