L11a535

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X₂₅₃₆ X_18,12,19,11 X_10,3,11,4 X_4,9,1,10 X_16,7,17,8 X_8,15,5,16 X_22,18,15,17 X_20,14,21,13 X_12,20,13,19 X_14,22,9,21
Gauss code	{1, -2, 4, -5}, {2, -1, 6, -7}, {5, -4, 3, -10, 9, -11}, {7, -6, 8, -3, 10, -9, 11, -8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 2 + v u 2 + 2 v 2 w u 2 -2 v w u 2 + 2 v 2 x u 2 - v x u 2 - v 2 w x u 2 + v w x u 2 + v 2 u -2 v u - v 2 w u + 3 v w u -2 w u -2 v 2 x u + 3 v x u + v 2 w x u -2 v w x u + w x u - x u + u + v - v w + 2 w -2 v x + v w x -2 w x + 2 x -1$ (db)
Jones polynomial	$q^{11/2}-4 q^{9/2}+7 q^{7/2}-11 q^{5/2}+13 q^{3/2}-15 \sqrt{q}+\frac{12}{\sqrt{q}}-\frac{12}{q^{3/2}}+\frac{6}{q^{5/2}}-\frac{5}{q^{7/2}}+\frac{1}{q^{9/2}}-\frac{1}{q^{11/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 7 a -1 + 3 a z 5 -4 z 5 a -1 + z 5 a -3 -3 a 3 z 3 + 12 a z 3 -6 z 3 a -1 + 2 z 3 a -3 + a 5 z -11 a 3 z + 16 a z -6 z a -1 + 3 a 5 z -1 -10 a 3 z -1 + 11 a z -1 -4 a -1 z -1 + a 5 z -3 -3 a 3 z -3 + 3 a z -3 - a -1 z -3$ (db)
Kauffman polynomial	$- a 2 z 10 - z 10 - a 3 z 9 -5 a z 9 -4 z 9 a -1 - a 4 z 8 + a 2 z 8 -7 z 8 a -2 -5 z 8 - a 5 z 7 - a 3 z 7 + 12 a z 7 + 4 z 7 a -1 -8 z 7 a -3 + 2 a 4 z 6 -2 a 2 z 6 + 10 z 6 a -2 -7 z 6 a -4 + 13 z 6 + 6 a 5 z 5 + 17 a 3 z 5 -2 a z 5 + 9 z 5 a -3 -4 z 5 a -5 + 6 a 4 z 4 + 19 a 2 z 4 -4 z 4 a -2 + 7 z 4 a -4 - z 4 a -6 + z 4 -13 a 5 z 3 -32 a 3 z 3 -16 a z 3 + 3 z 3 a -5 -17 a 4 z 2 -33 a 2 z 2 -16 z 2 + 13 a 5 z + 28 a 3 z + 21 a z + 3 z a -1 -3 z a -3 + 13 a 4 + 24 a 2 - a -2 + 11-6 a 5 z -1 -14 a 3 z -1 -12 a z -1 -3 a -1 z -1 + a -3 z -1 -3 a 4 z -2 -6 a 2 z -2 -3 z -2 + a 5 z -3 + 3 a 3 z -3 + 3 a z -3 + a -1 z -3$ (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 L11a535. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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