L11a195

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_10,4,11,3 X_22,10,7,9 X₂₇₃₈ X_18,13,19,14 X_6,12,1,11 X_20,15,21,16 X_14,19,15,20 X_4,18,5,17 X_16,6,17,5 X_12,21,13,22
Gauss code	{1, -4, 2, -9, 10, -6}, {4, -1, 3, -2, 6, -11, 5, -8, 7, -10, 9, -5, 8, -7, 11, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + 3 v u 4 -2 u 4 + 3 v 2 u 3 -8 v u 3 + 4 u 3 -4 v 2 u 2 + 9 v u 2 -4 u 2 + 4 v 2 u -8 v u + 3 u -2 v 2 + 3 v -1$ (db)
Jones polynomial	$q^{9/2}-3 q^{7/2}+6 q^{5/2}-12 q^{3/2}+15 \sqrt{q}-\frac{19}{\sqrt{q}}+\frac{19}{q^{3/2}}-\frac{17}{q^{5/2}}+\frac{13}{q^{7/2}}-\frac{8}{q^{9/2}}+\frac{4}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a z 7 -2 a 3 z 5 + 4 a z 5 -2 z 5 a -1 + a 5 z 3 -5 a 3 z 3 + 8 a z 3 -6 z 3 a -1 + z 3 a -3 + a 5 z -4 a 3 z + 8 a z -6 z a -1 + 2 z a -3 - a 3 z -1 + 3 a z -1 -2 a -1 z -1$ (db)
Kauffman polynomial	$- a 2 z 10 - z 10 -4 a 3 z 9 -7 a z 9 -3 z 9 a -1 -7 a 4 z 8 -12 a 2 z 8 -4 z 8 a -2 -9 z 8 -7 a 5 z 7 -5 a 3 z 7 + 4 a z 7 - z 7 a -1 -3 z 7 a -3 -4 a 6 z 6 + 7 a 4 z 6 + 24 a 2 z 6 + 8 z 6 a -2 - z 6 a -4 + 22 z 6 - a 7 z 5 + 11 a 5 z 5 + 19 a 3 z 5 + 15 a z 5 + 17 z 5 a -1 + 9 z 5 a -3 + 6 a 6 z 4 + 2 a 4 z 4 -12 a 2 z 4 -2 z 4 a -2 + 3 z 4 a -4 -13 z 4 + a 7 z 3 -5 a 5 z 3 -14 a 3 z 3 -21 a z 3 -22 z 3 a -1 -9 z 3 a -3 -2 a 6 z 2 -3 a 4 z 2 -3 a 2 z 2 -2 z 2 a -2 -2 z 2 a -4 -2 z 2 + a 5 z + 4 a 3 z + 11 a z + 12 z a -1 + 4 z a -3 + a 4 + 3 a 2 + 3- a 3 z -1 -3 a z -1 -2 a -1 z -1$ (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 L11a195. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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