L10a106

(Knotscape image)

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

Planar diagram presentation	X_10,1,11,2 X_18,11,19,12 X_20,5,9,6 X_14,7,15,8 X_12,4,13,3 X_16,14,17,13 X_6,15,7,16 X_8,9,1,10 X_4,19,5,20 X_2,18,3,17
Gauss code	{1, -10, 5, -9, 3, -7, 4, -8}, {8, -1, 2, -5, 6, -4, 7, -6, 10, -2, 9, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-\frac{u^3 v^3-2 u^3 v^2+u^3 v-3 u^2 v^3+7 u^2 v^2-5 u^2 v+2 u^2+2 u v^3-5 u v^2+7 u v-3 u+v^2-2 v+1}{u^{3/2} v^{3/2}}$ (db)
Jones polynomial	$q^{3/2}-4 \sqrt{q}+\frac{7}{\sqrt{q}}-\frac{11}{q^{3/2}}+\frac{13}{q^{5/2}}-\frac{14}{q^{7/2}}+\frac{13}{q^{9/2}}-\frac{11}{q^{11/2}}+\frac{6}{q^{13/2}}-\frac{3}{q^{15/2}}+\frac{1}{q^{17/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- z 3 a 7 -2 z a 7 + 2 z 5 a 5 + 6 z 3 a 5 + 5 z a 5 + a 5 z -1 - z 7 a 3 -4 z 5 a 3 -6 z 3 a 3 -5 z a 3 - a 3 z -1 + z 5 a + 2 z 3 a$ (db)
Kauffman polynomial	$- z 4 a 10 + z 2 a 10 -3 z 5 a 9 + 3 z 3 a 9 - z a 9 -5 z 6 a 8 + 4 z 4 a 8 - z 2 a 8 -7 z 7 a 7 + 10 z 5 a 7 -8 z 3 a 7 + z a 7 -6 z 8 a 6 + 7 z 6 a 6 -2 z 4 a 6 - z 2 a 6 -2 z 9 a 5 -10 z 7 a 5 + 33 z 5 a 5 -30 z 3 a 5 + 10 z a 5 - a 5 z -1 -11 z 8 a 4 + 24 z 6 a 4 -12 z 4 a 4 + z 2 a 4 + a 4 -2 z 9 a 3 -7 z 7 a 3 + 31 z 5 a 3 -27 z 3 a 3 + 9 z a 3 - a 3 z -1 -5 z 8 a 2 + 11 z 6 a 2 -3 z 4 a 2 - z 2 a 2 -4 z 7 a + 11 z 5 a -8 z 3 a + z a - z 6 + 2 z 4 - z 2$ (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 L10a106. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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