L11a502

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_10,3,11,4 X_20,15,21,16 X_14,5,15,6 X_4,13,5,14 X_12,19,7,20 X_18,11,19,12 X_22,17,13,18 X_16,21,17,22 X₂₇₃₈ X_6,9,1,10
Gauss code	{1, -10, 2, -5, 4, -11}, {10, -1, 11, -2, 7, -6}, {5, -4, 3, -9, 8, -7, 6, -3, 9, -8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 3 -2 v w 2 u 3 + w 2 u 3 - v u 3 -2 v 2 w u 3 + 3 v w u 3 - w u 3 - v 2 u 2 + 2 v w 2 u 2 - w 2 u 2 + 2 v u 2 + 2 v 2 w u 2 -4 v w u 2 + 2 w u 2 + v 2 u -2 v w 2 u + w 2 u -2 v u -2 v 2 w u + 4 v w u -2 w u - v 2 + v w 2 - w 2 + 2 v + v 2 w -3 v w + 2 w$ (db)
Jones polynomial	$q -3 -2 q -4 + 6 q -5 -9 q -6 + 14 q -7 -15 q -8 + 17 q -9 -14 q -10 + 11 q -11 -7 q -12 + 3 q -13 - q -14$ (db)
Signature	-6 (db)
HOMFLY-PT polynomial	$- a 14 z -2 - z 4 a 12 - z 2 a 12 + 4 a 12 z -2 + 4 a 12 + z 6 a 10 + z 4 a 10 -6 z 2 a 10 -5 a 10 z -2 -10 a 10 + 2 z 6 a 8 + 7 z 4 a 8 + 7 z 2 a 8 + 2 a 8 z -2 + 4 a 8 + z 6 a 6 + 4 z 4 a 6 + 5 z 2 a 6 + 2 a 6$ (db)
Kauffman polynomial	$z 5 a 17 -2 z 3 a 17 + 3 z 6 a 16 -5 z 4 a 16 + 6 z 7 a 15 -14 z 5 a 15 + 12 z 3 a 15 -5 z a 15 + a 15 z -1 + 7 z 8 a 14 -18 z 6 a 14 + 22 z 4 a 14 -12 z 2 a 14 - a 14 z -2 + 4 a 14 + 4 z 9 a 13 -2 z 7 a 13 -13 z 5 a 13 + 30 z 3 a 13 -21 z a 13 + 5 a 13 z -1 + z 10 a 12 + 9 z 8 a 12 -30 z 6 a 12 + 44 z 4 a 12 -33 z 2 a 12 -4 a 12 z -2 + 17 a 12 + 6 z 9 a 11 -8 z 7 a 11 -9 z 5 a 11 + 35 z 3 a 11 -33 z a 11 + 9 a 11 z -1 + z 10 a 10 + 5 z 8 a 10 -17 z 6 a 10 + 27 z 4 a 10 -33 z 2 a 10 -5 a 10 z -2 + 20 a 10 + 2 z 9 a 9 + 2 z 7 a 9 -16 z 5 a 9 + 21 z 3 a 9 -16 z a 9 + 5 a 9 z -1 + 3 z 8 a 8 -7 z 6 a 8 + 6 z 4 a 8 -7 z 2 a 8 -2 a 8 z -2 + 6 a 8 + 2 z 7 a 7 -5 z 5 a 7 + 2 z 3 a 7 + z a 7 + z 6 a 6 -4 z 4 a 6 + 5 z 2 a 6 -2 a 6$ (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 =

-6 is the signature of L11a502. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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