L11a105

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 5 + 2 u 5 + 4 v u 4 -6 u 4 -6 v u 3 + 6 u 3 + 6 v u 2 -6 u 2 -6 v u + 4 u + 2 v -1$ (db)
Jones polynomial	$q^{11/2}-4 q^{9/2}+7 q^{7/2}-11 q^{5/2}+15 q^{3/2}-16 \sqrt{q}+\frac{15}{\sqrt{q}}-\frac{13}{q^{3/2}}+\frac{9}{q^{5/2}}-\frac{6}{q^{7/2}}+\frac{2}{q^{9/2}}-\frac{1}{q^{11/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 7 a -1 + 3 a z 5 -4 z 5 a -1 + z 5 a -3 -3 a 3 z 3 + 10 a z 3 -6 z 3 a -1 + 2 z 3 a -3 + a 5 z -8 a 3 z + 9 a z -4 z a -1 + 2 a 5 z -1 -4 a 3 z -1 + 3 a z -1 - a -1 z -1$ (db)
Kauffman polynomial	$- a 2 z 10 - z 10 -2 a 3 z 9 -6 a z 9 -4 z 9 a -1 -2 a 4 z 8 -4 a 2 z 8 -7 z 8 a -2 -9 z 8 - a 5 z 7 + 2 a 3 z 7 + 9 a z 7 -2 z 7 a -1 -8 z 7 a -3 + 7 a 4 z 6 + 18 a 2 z 6 + 5 z 6 a -2 -7 z 6 a -4 + 23 z 6 + 5 a 5 z 5 + 13 a 3 z 5 + 13 a z 5 + 16 z 5 a -1 + 7 z 5 a -3 -4 z 5 a -5 -6 a 4 z 4 -12 a 2 z 4 + 7 z 4 a -2 + 7 z 4 a -4 - z 4 a -6 -7 z 4 -9 a 5 z 3 -25 a 3 z 3 -25 a z 3 -11 z 3 a -1 + z 3 a -3 + 3 z 3 a -5 - a 4 z 2 -3 a 2 z 2 -7 z 2 a -2 -2 z 2 a -4 -7 z 2 + 7 a 5 z + 16 a 3 z + 13 a z + 3 z a -1 - z a -3 + 2 a 4 + 3 a 2 + a -2 + 3-2 a 5 z -1 -4 a 3 z -1 -3 a z -1 - a -1 z -1$ (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 L11a105. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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