L11a134

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- u 5 -4 v u 4 + 6 u 4 + 10 v u 3 -12 u 3 -12 v u 2 + 10 u 2 + 6 v u -4 u - v$ (db)
Jones polynomial	$q^{5/2}-4 q^{3/2}+9 \sqrt{q}-\frac{14}{\sqrt{q}}+\frac{18}{q^{3/2}}-\frac{22}{q^{5/2}}+\frac{20}{q^{7/2}}-\frac{18}{q^{9/2}}+\frac{13}{q^{11/2}}-\frac{8}{q^{13/2}}+\frac{4}{q^{15/2}}-\frac{1}{q^{17/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z 3 a 7 - a 7 z -1 - z 5 a 5 + z 3 a 5 + 5 z a 5 + 4 a 5 z -1 -3 z 5 a 3 -8 z 3 a 3 -10 z a 3 -4 a 3 z -1 - z 5 a + z 3 a + 3 z a + a z -1 + z 3 a -1$ (db)
Kauffman polynomial	$-2 a 6 z 10 -2 a 4 z 10 -5 a 7 z 9 -12 a 5 z 9 -7 a 3 z 9 -4 a 8 z 8 -8 a 6 z 8 -16 a 4 z 8 -12 a 2 z 8 - a 9 z 7 + 13 a 7 z 7 + 23 a 5 z 7 -4 a 3 z 7 -13 a z 7 + 14 a 8 z 6 + 39 a 6 z 6 + 47 a 4 z 6 + 13 a 2 z 6 -9 z 6 + 3 a 9 z 5 -4 a 7 z 5 + 8 a 5 z 5 + 37 a 3 z 5 + 18 a z 5 -4 z 5 a -1 -15 a 8 z 4 -35 a 6 z 4 -24 a 4 z 4 + 5 a 2 z 4 - z 4 a -2 + 8 z 4 -3 a 9 z 3 -8 a 7 z 3 -27 a 5 z 3 -34 a 3 z 3 -11 a z 3 + z 3 a -1 + 4 a 8 z 2 + 2 a 6 z 2 -8 a 4 z 2 -9 a 2 z 2 -3 z 2 + a 9 z + 4 a 7 z + 14 a 5 z + 15 a 3 z + 4 a z + a 8 + 4 a 6 + 7 a 4 + 4 a 2 + 1- a 7 z -1 -4 a 5 z -1 -4 a 3 z -1 - a z -1$ (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 L11a134. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -8$	${\mathbb Z}$
$r = -7$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -5$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -4$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{9}$
$r = -3$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = -1$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 0$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{8}$
$r = 1$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 2$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 3$	${\mathbb Z}_2$	${\mathbb Z}$