L11a487

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,7,15,8 X_4,15,1,16 X_22,10,19,9 X₈₄₉₃ X_16,21,17,22 X_18,11,5,12 X_20,5,21,6 X_10,17,11,18 X_12,20,13,19 X_2,14,3,13
Gauss code	{1, -11, 5, -3}, {10, -8, 6, -4}, {8, -1, 2, -5, 4, -9, 7, -10, 11, -2, 3, -6, 9, -7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 5 - v w u 5 + w u 5 - u 5 -4 v u 4 + 4 v w u 4 -4 w u 4 + 4 u 4 + 7 v u 3 -7 v w u 3 + 7 w u 3 -7 u 3 -7 v u 2 + 7 v w u 2 -7 w u 2 + 7 u 2 + 4 v u -4 v w u + 4 w u -4 u - v + v w - w + 1$ (db)
Jones polynomial	$q 3 -5 q 2 + 12 q -18 + 28 q -1 -30 q -2 + 32 q -3 -27 q -4 + 20 q -5 -13 q -6 + 5 q -7 - q -8$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$- a 2 z 8 + 2 a 4 z 6 -4 a 2 z 6 + z 6 - a 6 z 4 + 5 a 4 z 4 -6 a 2 z 4 + 2 z 4 - a 6 z 2 + 4 a 4 z 2 -4 a 2 z 2 + z 2 - a 6 + 4 a 4 -5 a 2 + 2- a 6 z -2 + 4 a 4 z -2 -5 a 2 z -2 + 2 z -2$ (db)
Kauffman polynomial	$4 a 4 z 10 + 4 a 2 z 10 + 13 a 5 z 9 + 24 a 3 z 9 + 11 a z 9 + 18 a 6 z 8 + 28 a 4 z 8 + 21 a 2 z 8 + 11 z 8 + 13 a 7 z 7 -4 a 5 z 7 -38 a 3 z 7 -16 a z 7 + 5 z 7 a -1 + 5 a 8 z 6 -27 a 6 z 6 -72 a 4 z 6 -65 a 2 z 6 + z 6 a -2 -24 z 6 + a 9 z 5 -16 a 7 z 5 -23 a 5 z 5 + 3 a 3 z 5 + a z 5 -8 z 5 a -1 -2 a 8 z 4 + 14 a 6 z 4 + 49 a 4 z 4 + 51 a 2 z 4 - z 4 a -2 + 17 z 4 + 7 a 7 z 3 + 18 a 5 z 3 + 14 a 3 z 3 + 5 a z 3 + 2 z 3 a -1 -4 a 6 z 2 -13 a 4 z 2 -13 a 2 z 2 -4 z 2 -3 a 7 z -10 a 5 z -12 a 3 z -5 a z + a 6 + 4 a 4 + 5 a 2 + 3 + a 7 z -1 + 5 a 5 z -1 + 9 a 3 z -1 + 5 a z -1 - a 6 z -2 -4 a 4 z -2 -5 a 2 z -2 -2 z -2$ (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 =

-2 is the signature of L11a487. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -3$	$i = -1$
$r = -7$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -4$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -3$	${\mathbb Z}^{16}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = -2$	${\mathbb Z}^{16}\oplus{\mathbb Z}_2^{16}$	${\mathbb Z}^{16}$
$r = -1$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{16}$	${\mathbb Z}^{16}$
$r = 0$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{14}$	${\mathbb Z}^{18}$
$r = 1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 3$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 4$	${\mathbb Z}_2$	${\mathbb Z}$