L11a201

(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_16,5,17,6 X_22,18,7,17 X_18,12,19,11 X_12,22,13,21 X_20,14,21,13 X_14,20,15,19 X₆₇₁₈ X_4,15,5,16
Gauss code	{1, -2, 3, -11, 4, -10}, {10, -1, 2, -3, 6, -7, 8, -9, 11, -4, 5, -6, 9, -8, 7, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 4 + 5 v 2 u 3 -4 v u 3 -4 v 2 u 2 + 7 v u 2 -4 u 2 -4 v u + 5 u -2$ (db)
Jones polynomial	$q^{7/2}-2 q^{5/2}+4 q^{3/2}-7 \sqrt{q}+\frac{9}{\sqrt{q}}-\frac{11}{q^{3/2}}+\frac{11}{q^{5/2}}-\frac{11}{q^{7/2}}+\frac{8}{q^{9/2}}-\frac{6}{q^{11/2}}+\frac{3}{q^{13/2}}-\frac{1}{q^{15/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- a 3 z 7 - a z 7 + a 5 z 5 -4 a 3 z 5 -5 a z 5 + z 5 a -1 + 3 a 5 z 3 -4 a 3 z 3 -9 a z 3 + 4 z 3 a -1 + 2 a 5 z - a 3 z -8 a z + 4 z a -1 + a 5 z -1 -2 a z -1 + a -1 z -1$ (db)
Kauffman polynomial	$- a 2 z 10 - z 10 -4 a 3 z 9 -6 a z 9 -2 z 9 a -1 -7 a 4 z 8 -6 a 2 z 8 - z 8 a -2 -9 a 5 z 7 + 6 a 3 z 7 + 26 a z 7 + 11 z 7 a -1 -8 a 6 z 6 + 14 a 4 z 6 + 34 a 2 z 6 + 6 z 6 a -2 + 18 z 6 -6 a 7 z 5 + 18 a 5 z 5 + 9 a 3 z 5 -35 a z 5 -20 z 5 a -1 -3 a 8 z 4 + 10 a 6 z 4 - a 4 z 4 -41 a 2 z 4 -12 z 4 a -2 -39 z 4 - a 9 z 3 + 5 a 7 z 3 -10 a 5 z 3 -9 a 3 z 3 + 21 a z 3 + 14 z 3 a -1 -2 a 6 z 2 -3 a 4 z 2 + 16 a 2 z 2 + 9 z 2 a -2 + 26 z 2 -2 a 7 z + 5 a 5 z + a 3 z -10 a z -4 z a -1 + a 4 -3 a 2 -2 a -2 -5- a 5 z -1 + 2 a z -1 + a -1 z -1$ (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 =

-3 is the signature of L11a201. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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