L11a184

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 4 + 3 v u 4 - u 4 + 6 v 2 u 3 -10 v u 3 + 4 u 3 -7 v 2 u 2 + 15 v u 2 -7 u 2 + 4 v 2 u -10 v u + 6 u - v 2 + 3 v -2$ (db)
Jones polynomial	$-q^{7/2}+4 q^{5/2}-9 q^{3/2}+16 \sqrt{q}-\frac{23}{\sqrt{q}}+\frac{25}{q^{3/2}}-\frac{27}{q^{5/2}}+\frac{23}{q^{7/2}}-\frac{17}{q^{9/2}}+\frac{11}{q^{11/2}}-\frac{5}{q^{13/2}}+\frac{1}{q^{15/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a 3 z 7 + a z 7 - a 5 z 5 + 2 a 3 z 5 + 3 a z 5 - z 5 a -1 - a 5 z 3 - a 3 z 3 + 4 a z 3 -2 z 3 a -1 + a 5 z -3 a 3 z + 2 a z - z a -1 + a 3 z -1 - a z -1$ (db)
Kauffman polynomial	$-3 a 4 z 10 -3 a 2 z 10 -9 a 5 z 9 -17 a 3 z 9 -8 a z 9 -10 a 6 z 8 -16 a 4 z 8 -16 a 2 z 8 -10 z 8 -5 a 7 z 7 + 12 a 5 z 7 + 26 a 3 z 7 + a z 7 -8 z 7 a -1 - a 8 z 6 + 22 a 6 z 6 + 47 a 4 z 6 + 39 a 2 z 6 -4 z 6 a -2 + 11 z 6 + 9 a 7 z 5 + 5 a 5 z 5 + 16 a z 5 + 11 z 5 a -1 - z 5 a -3 + a 8 z 4 -12 a 6 z 4 -29 a 4 z 4 -23 a 2 z 4 + 5 z 4 a -2 -2 z 4 -3 a 7 z 3 -7 a 5 z 3 -12 a 3 z 3 -16 a z 3 -7 z 3 a -1 + z 3 a -3 + 2 a 4 z 2 + 2 a 2 z 2 -2 z 2 a -2 -2 z 2 + 2 a 5 z + 5 a 3 z + 5 a z + 2 z a -1 - a 2 + a 3 z -1 + a z -1$ (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 L11a184. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -7$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -4$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = -3$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = -2$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{14}$
$r = -1$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = 0$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{13}$
$r = 1$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 2$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$