L11a103

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_20,7,21,8 X_4,21,1,22 X_14,6,15,5 X_12,4,13,3 X_22,14,5,13 X_18,9,19,10 X_16,11,17,12 X_2,16,3,15 X_10,17,11,18 X_8,19,9,20
Gauss code	{1, -9, 5, -3}, {4, -1, 2, -11, 7, -10, 8, -5, 6, -4, 9, -8, 10, -7, 11, -2, 3, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-3 v u 3 + 3 u 3 + 6 v u 2 -6 u 2 -6 v u + 6 u + 3 v -3$ (db)
Jones polynomial	$-q^{9/2}+3 q^{7/2}-6 q^{5/2}+7 q^{3/2}-10 \sqrt{q}+\frac{11}{\sqrt{q}}-\frac{10}{q^{3/2}}+\frac{9}{q^{5/2}}-\frac{7}{q^{7/2}}+\frac{4}{q^{9/2}}-\frac{3}{q^{11/2}}+\frac{1}{q^{13/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 3 a 5 - z a 5 + a 5 z -1 + z 5 a 3 + 2 z 3 a 3 -2 a 3 z -1 + z 5 a + z 3 a + a z -1 + z 5 a -1 + 2 z 3 a -1 + 2 z a -1 + a -1 z -1 - z 3 a -3 - z a -3 - a -3 z -1$ (db)
Kauffman polynomial	$-2 a 4 z 10 -2 a 2 z 10 -3 a 5 z 9 -8 a 3 z 9 -5 a z 9 - a 6 z 8 + 7 a 4 z 8 + a 2 z 8 -7 z 8 + 17 a 5 z 7 + 38 a 3 z 7 + 14 a z 7 -7 z 7 a -1 + 5 a 6 z 6 + 20 a 2 z 6 -7 z 6 a -2 + 18 z 6 -30 a 5 z 5 -51 a 3 z 5 -5 a z 5 + 10 z 5 a -1 -6 z 5 a -3 -7 a 6 z 4 -13 a 4 z 4 -29 a 2 z 4 + 8 z 4 a -2 -3 z 4 a -4 -12 z 4 + 17 a 5 z 3 + 15 a 3 z 3 -6 a z 3 + 3 z 3 a -1 + 6 z 3 a -3 - z 3 a -5 + 3 a 6 z 2 + 6 a 4 z 2 + 10 a 2 z 2 + 7 z 2 + a 5 z + 7 a 3 z + 6 a z -3 z a -1 -3 z a -3 - a 4 -3 a 2 - a -2 -2- a 5 z -1 -2 a 3 z -1 - a z -1 + a -1 z -1 + a -3 z -1$ (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 L11a103. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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