L11a170

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_10,4,11,3 X_12,7,13,8 X_22,15,7,16 X_14,6,15,5 X_6,14,1,13 X_16,21,17,22 X_18,10,19,9 X_20,11,21,12 X_4,18,5,17 X_2,19,3,20
Gauss code	{1, -11, 2, -10, 5, -6}, {3, -1, 8, -2, 9, -3, 6, -5, 4, -7, 10, -8, 11, -9, 7, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + 3 v u 4 -2 u 4 + 5 v 2 u 3 -11 v u 3 + 6 u 3 -8 v 2 u 2 + 15 v u 2 -8 u 2 + 6 v 2 u -11 v u + 5 u -2 v 2 + 3 v -1$ (db)
Jones polynomial	$q^{9/2}-5 q^{7/2}+11 q^{5/2}-19 q^{3/2}+24 \sqrt{q}-\frac{29}{\sqrt{q}}+\frac{28}{q^{3/2}}-\frac{24}{q^{5/2}}+\frac{18}{q^{7/2}}-\frac{10}{q^{9/2}}+\frac{4}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a z 7 -2 a 3 z 5 + 2 a z 5 -2 z 5 a -1 + a 5 z 3 -3 a 3 z 3 + a z 3 -2 z 3 a -1 + z 3 a -3 + a 5 z - a 3 z - a z + 2 z a -1 + a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$-4 a 2 z 10 -4 z 10 -11 a 3 z 9 -21 a z 9 -10 z 9 a -1 -13 a 4 z 8 -17 a 2 z 8 -10 z 8 a -2 -14 z 8 -9 a 5 z 7 + 11 a 3 z 7 + 39 a z 7 + 14 z 7 a -1 -5 z 7 a -3 -4 a 6 z 6 + 21 a 4 z 6 + 48 a 2 z 6 + 20 z 6 a -2 - z 6 a -4 + 44 z 6 - a 7 z 5 + 12 a 5 z 5 -21 a z 5 + z 5 a -1 + 9 z 5 a -3 + 4 a 6 z 4 -17 a 4 z 4 -38 a 2 z 4 -10 z 4 a -2 + z 4 a -4 -28 z 4 + a 7 z 3 -7 a 5 z 3 -2 a 3 z 3 + 10 a z 3 -4 z 3 a -3 - a 6 z 2 + 6 a 4 z 2 + 12 a 2 z 2 + z 2 a -2 + 6 z 2 + a 5 z - a 3 z -5 a z -4 z a -1 - z a -3 - a -2 + a -1 z -1 + a -3 z -1$ (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 L11a170. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -3$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = -2$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = -1$	${\mathbb Z}^{15}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = 0$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{15}$	${\mathbb Z}^{16}$
$r = 1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = 2$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{12}$
$r = 3$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$