L11a102

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 5 + 2 u 5 + 5 v u 4 -5 u 4 -8 v u 3 + 8 u 3 + 8 v u 2 -8 u 2 -5 v u + 5 u + 2 v -2$ (db)
Jones polynomial	$-q^{7/2}+3 q^{5/2}-7 q^{3/2}+11 \sqrt{q}-\frac{17}{\sqrt{q}}+\frac{19}{q^{3/2}}-\frac{19}{q^{5/2}}+\frac{17}{q^{7/2}}-\frac{13}{q^{9/2}}+\frac{8}{q^{11/2}}-\frac{4}{q^{13/2}}+\frac{1}{q^{15/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a 3 z 7 + a z 7 - a 5 z 5 + 3 a 3 z 5 + 4 a z 5 - z 5 a -1 -2 a 5 z 3 + a 3 z 3 + 7 a z 3 -3 z 3 a -1 -4 a 3 z + 7 a z -3 z a -1 + a 5 z -1 -3 a 3 z -1 + 4 a z -1 -2 a -1 z -1$ (db)
Kauffman polynomial	$-2 a 4 z 10 -2 a 2 z 10 -5 a 5 z 9 -10 a 3 z 9 -5 a z 9 -6 a 6 z 8 -5 a 4 z 8 -6 a 2 z 8 -7 z 8 -4 a 7 z 7 + 7 a 5 z 7 + 21 a 3 z 7 + 4 a z 7 -6 z 7 a -1 - a 8 z 6 + 13 a 6 z 6 + 13 a 4 z 6 + 17 a 2 z 6 -3 z 6 a -2 + 15 z 6 + 10 a 7 z 5 - a 5 z 5 -17 a 3 z 5 + 9 a z 5 + 14 z 5 a -1 - z 5 a -3 + 2 a 8 z 4 -5 a 6 z 4 -12 a 2 z 4 + 5 z 4 a -2 -14 z 4 -6 a 7 z 3 + 6 a 5 z 3 + 3 a 3 z 3 -25 a z 3 -14 z 3 a -1 + 2 z 3 a -3 - a 8 z 2 - a 6 z 2 -5 a 4 z 2 -4 a 2 z 2 + z 2 - a 7 z -2 a 5 z + 7 a 3 z + 15 a z + 7 z a -1 + a 6 + 3 a 4 + 3 a 2 + 2- a 5 z -1 -3 a 3 z -1 -4 a z -1 -2 a -1 z -1$ (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 L11a102. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -7$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -4$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -3$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = -2$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -1$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 0$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{11}$
$r = 1$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 2$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$