L11a145

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 4 + 2 v u 4 + 5 v 2 u 3 -7 v u 3 + 2 u 3 -5 v 2 u 2 + 9 v u 2 -5 u 2 + 2 v 2 u -7 v u + 5 u + 2 v -2$ (db)
Jones polynomial	$q^{3/2}-4 \sqrt{q}+\frac{7}{\sqrt{q}}-\frac{12}{q^{3/2}}+\frac{15}{q^{5/2}}-\frac{18}{q^{7/2}}+\frac{17}{q^{9/2}}-\frac{15}{q^{11/2}}+\frac{11}{q^{13/2}}-\frac{6}{q^{15/2}}+\frac{3}{q^{17/2}}-\frac{1}{q^{19/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$z 5 a 7 + 3 z 3 a 7 + 2 z a 7 - z 7 a 5 -4 z 5 a 5 -6 z 3 a 5 -4 z a 5 - z 7 a 3 -3 z 5 a 3 - z 3 a 3 + 2 z a 3 + a 3 z -1 + z 5 a + 2 z 3 a - z a - a z -1$ (db)
Kauffman polynomial	$- z 5 a 11 + 2 z 3 a 11 -3 z 6 a 10 + 6 z 4 a 10 -2 z 2 a 10 -5 z 7 a 9 + 10 z 5 a 9 -6 z 3 a 9 + z a 9 -6 z 8 a 8 + 13 z 6 a 8 -13 z 4 a 8 + 4 z 2 a 8 -5 z 9 a 7 + 10 z 7 a 7 -12 z 5 a 7 + 5 z 3 a 7 - z a 7 -2 z 10 a 6 -4 z 8 a 6 + 19 z 6 a 6 -28 z 4 a 6 + 12 z 2 a 6 -10 z 9 a 5 + 29 z 7 a 5 -38 z 5 a 5 + 23 z 3 a 5 -5 z a 5 -2 z 10 a 4 -4 z 8 a 4 + 20 z 6 a 4 -21 z 4 a 4 + 8 z 2 a 4 -5 z 9 a 3 + 10 z 7 a 3 -4 z 5 a 3 + 4 z 3 a 3 -4 z a 3 + a 3 z -1 -6 z 8 a 2 + 16 z 6 a 2 -10 z 4 a 2 + 2 z 2 a 2 - a 2 -4 z 7 a + 11 z 5 a -6 z 3 a - z a + a z -1 - z 6 + 2 z 4$ (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 L11a145. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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