L10a147

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 3 - v u 3 - v 2 w u 3 + v w u 3 + v 3 u 2 -3 v 2 u 2 + 4 v u 2 - v 3 w u 2 + 3 v 2 w u 2 -3 v w u 2 + w u 2 - u 2 - v 3 u + 3 v 2 u -3 v u + v 3 w u -4 v 2 w u + 3 v w u - w u + u - v 2 + v + v 2 w - v w$ (db)
Jones polynomial	$q 6 -3 q 5 + 6 q 4 -9 q 3 + 14 q 2 -13 q + 14-11 q -1 + 8 q -2 -4 q -3 + q -4$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 6 a -2 - z 6 + a 2 z 4 -3 z 4 a -2 + z 4 a -4 -2 z 4 + a 2 z 2 -4 z 2 a -2 + 2 z 2 a -4 -3 a -2 + a -4 + 2-2 a -2 z -2 + a -4 z -2 + z -2$ (db)
Kauffman polynomial	$2 z 9 a -1 + 2 z 9 a -3 + 10 z 8 a -2 + 4 z 8 a -4 + 6 z 8 + 9 a z 7 + 8 z 7 a -1 + 2 z 7 a -3 + 3 z 7 a -5 + 8 a 2 z 6 -23 z 6 a -2 -11 z 6 a -4 + z 6 a -6 -3 z 6 + 4 a 3 z 5 -11 a z 5 -19 z 5 a -1 -13 z 5 a -3 -9 z 5 a -5 + a 4 z 4 -9 a 2 z 4 + 20 z 4 a -2 + 11 z 4 a -4 -3 z 4 a -6 -4 z 4 -2 a 3 z 3 + 3 a z 3 + 8 z 3 a -1 + 10 z 3 a -3 + 7 z 3 a -5 + 3 a 2 z 2 -13 z 2 a -2 -7 z 2 a -4 + 2 z 2 a -6 - z 2 -3 z a -1 -3 z a -3 + 5 a -2 + 3 a -4 + 3 + 2 a -1 z -1 + 2 a -3 z -1 -2 a -2 z -2 - a -4 z -2 - z -2$ (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 =

0 is the signature of L10a147. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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