L10a160

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 2 u 3 - v 2 w u 3 + v w u 3 - v 2 u 2 - v 2 w 2 u 2 + v w 2 u 2 + v u 2 + 2 v 2 w u 2 -2 v w u 2 + w u 2 - v w 2 u + w 2 u - v u - v 2 w u + 2 v w u -2 w u + u - w 2 - v w + w$ (db)
Jones polynomial	$q 10 -2 q 9 + 4 q 8 -6 q 7 + 8 q 6 -7 q 5 + 8 q 4 -5 q 3 + 4 q 2 -2 q + 1$ (db)
Signature	4 (db)
HOMFLY-PT polynomial	$- z 6 a -4 - z 6 a -6 + z 4 a -2 -3 z 4 a -4 -4 z 4 a -6 + z 4 a -8 + 3 z 2 a -2 -6 z 2 a -6 + 3 z 2 a -8 + a -2 + 3 a -4 -6 a -6 + 2 a -8 + a -4 z -2 -2 a -6 z -2 + a -8 z -2$ (db)
Kauffman polynomial	$z 9 a -5 + z 9 a -7 + 2 z 8 a -4 + 5 z 8 a -6 + 3 z 8 a -8 + 2 z 7 a -3 + z 7 a -7 + 3 z 7 a -9 + z 6 a -2 -6 z 6 a -4 -20 z 6 a -6 -10 z 6 a -8 + 3 z 6 a -10 -7 z 5 a -3 -8 z 5 a -5 -9 z 5 a -7 -6 z 5 a -9 + 2 z 5 a -11 -4 z 4 a -2 + 5 z 4 a -4 + 35 z 4 a -6 + 19 z 4 a -8 -6 z 4 a -10 + z 4 a -12 + 5 z 3 a -3 + 12 z 3 a -5 + 16 z 3 a -7 + 6 z 3 a -9 -3 z 3 a -11 + 4 z 2 a -2 -6 z 2 a -4 -31 z 2 a -6 -14 z 2 a -8 + 5 z 2 a -10 -2 z 2 a -12 -9 z a -5 -9 z a -7 - a -2 + 5 a -4 + 11 a -6 + 5 a -8 - a -10 + 2 a -5 z -1 + 2 a -7 z -1 - a -4 z -2 -2 a -6 z -2 - a -8 z -2$ (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 =

4 is the signature of L10a160. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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