L11a104

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_2,9,3,10 X_12,3,13,4 X_20,11,21,12 X_18,6,19,5 X_22,20,5,19 X_10,21,11,22 X_4,17,1,18 X_16,14,17,13 X_14,8,15,7 X_8,16,9,15
Gauss code	{1, -2, 3, -8}, {5, -1, 10, -11, 2, -7, 4, -3, 9, -10, 11, -9, 8, -5, 6, -4, 7, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 5 + 6 v u 4 -4 u 4 -12 v u 3 + 12 u 3 + 12 v u 2 -12 u 2 -4 v u + 6 u -1$ (db)
Jones polynomial	$q^{9/2}-5 q^{7/2}+10 q^{5/2}-15 q^{3/2}+20 \sqrt{q}-\frac{23}{\sqrt{q}}+\frac{22}{q^{3/2}}-\frac{19}{q^{5/2}}+\frac{13}{q^{7/2}}-\frac{8}{q^{9/2}}+\frac{3}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a z 7 -2 a 3 z 5 + 4 a z 5 -2 z 5 a -1 + a 5 z 3 -6 a 3 z 3 + 9 a z 3 -4 z 3 a -1 + z 3 a -3 + 2 a 5 z -9 a 3 z + 8 a z -3 z a -1 + 2 a 5 z -1 -4 a 3 z -1 + 3 a z -1 - a -1 z -1$ (db)
Kauffman polynomial	$-2 a 2 z 10 -2 z 10 -5 a 3 z 9 -12 a z 9 -7 z 9 a -1 -7 a 4 z 8 -12 a 2 z 8 -9 z 8 a -2 -14 z 8 -6 a 5 z 7 -4 a 3 z 7 + 15 a z 7 + 8 z 7 a -1 -5 z 7 a -3 -3 a 6 z 6 + 8 a 4 z 6 + 27 a 2 z 6 + 21 z 6 a -2 - z 6 a -4 + 38 z 6 - a 7 z 5 + 10 a 5 z 5 + 24 a 3 z 5 + 11 a z 5 + 8 z 5 a -1 + 10 z 5 a -3 + 4 a 6 z 4 -3 a 4 z 4 -14 a 2 z 4 -11 z 4 a -2 + z 4 a -4 -19 z 4 + 2 a 7 z 3 -10 a 5 z 3 -32 a 3 z 3 -24 a z 3 -7 z 3 a -1 -3 z 3 a -3 - a 6 z 2 -2 a 4 z 2 -4 a 2 z 2 - z 2 a -2 -4 z 2 - a 7 z + 7 a 5 z + 18 a 3 z + 13 a z + 2 z a -1 - z a -3 + 2 a 4 + 3 a 2 + a -2 + 3-2 a 5 z -1 -4 a 3 z -1 -3 a z -1 - a -1 z -1$ (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 L11a104. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{3}$
$r = -3$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = -1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 0$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{12}$
$r = 1$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 2$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 3$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$