L11a346

(Knotscape image)

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

Planar diagram presentation	X_12,1,13,2 X₈₄₉₃ X_20,14,21,13 X_22,17,11,18 X_18,21,19,22 X_6,16,7,15 X_16,8,17,7 X_14,20,15,19 X_10,6,1,5 X_4,10,5,9 X_2,11,3,12
Gauss code	{1, -11, 2, -10, 9, -6, 7, -2, 10, -9}, {11, -1, 3, -8, 6, -7, 4, -5, 8, -3, 5, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 3 u 3 + 5 v 2 u 3 -5 v u 3 + u 3 + v 3 u 2 -6 v 2 u 2 + 6 v u 2 - u 2 - v 3 u + 6 v 2 u -6 v u + u + v 3 -5 v 2 + 5 v -1$ (db)
Jones polynomial	$q^{17/2}-3 q^{15/2}+7 q^{13/2}-12 q^{11/2}+15 q^{9/2}-17 q^{7/2}+16 q^{5/2}-14 q^{3/2}+10 \sqrt{q}-\frac{6}{\sqrt{q}}+\frac{2}{q^{3/2}}-\frac{1}{q^{5/2}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$z 7 a -3 -2 z 5 a -1 + 4 z 5 a -3 -2 z 5 a -5 + a z 3 -7 z 3 a -1 + 8 z 3 a -3 -6 z 3 a -5 + z 3 a -7 + 3 a z -9 z a -1 + 11 z a -3 -7 z a -5 + 2 z a -7 + 2 a z -1 -5 a -1 z -1 + 6 a -3 z -1 -4 a -5 z -1 + a -7 z -1$ (db)
Kauffman polynomial	$- z 10 a -2 - z 10 a -4 -2 z 9 a -1 -6 z 9 a -3 -4 z 9 a -5 -5 z 8 a -2 -11 z 8 a -4 -8 z 8 a -6 -2 z 8 - a z 7 + z 7 a -1 + 4 z 7 a -3 -7 z 7 a -5 -9 z 7 a -7 + 20 z 6 a -2 + 28 z 6 a -4 + 9 z 6 a -6 -6 z 6 a -8 + 7 z 6 + 5 a z 5 + 17 z 5 a -1 + 31 z 5 a -3 + 37 z 5 a -5 + 15 z 5 a -7 -3 z 5 a -9 -13 z 4 a -2 -10 z 4 a -4 + 3 z 4 a -6 + 6 z 4 a -8 - z 4 a -10 -7 z 4 -9 a z 3 -33 z 3 a -1 -48 z 3 a -3 -41 z 3 a -5 -15 z 3 a -7 + 2 z 3 a -9 - z 2 a -2 -6 z 2 a -4 -9 z 2 a -6 -4 z 2 a -8 + z 2 a -10 + z 2 + 7 a z + 22 z a -1 + 29 z a -3 + 20 z a -5 + 6 z a -7 + a -2 + 3 a -4 + 3 a -6 + a -8 + 1-2 a z -1 -5 a -1 z -1 -6 a -3 z -1 -4 a -5 z -1 - a -7 z -1$ (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 =

3 is the signature of L11a346. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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