L10a60

(Knotscape image)

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

Visit L10a60's page at the original Knot Atlas.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + v u 4 + 3 v 2 u 3 -4 v u 3 + 2 u 3 -4 v 2 u 2 + 7 v u 2 -4 u 2 + 2 v 2 u -4 v u + 3 u + v -1$ (db)
Jones polynomial	$q^{11/2}-3 q^{9/2}+6 q^{7/2}-10 q^{5/2}+11 q^{3/2}-13 \sqrt{q}+\frac{11}{\sqrt{q}}-\frac{9}{q^{3/2}}+\frac{6}{q^{5/2}}-\frac{3}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 7 a -1 + 2 a z 5 -5 z 5 a -1 + z 5 a -3 - a 3 z 3 + 7 a z 3 -10 z 3 a -1 + 3 z 3 a -3 -2 a 3 z + 8 a z -8 z a -1 + 3 z a -3 - a 3 z -1 + 3 a z -1 -2 a -1 z -1$ (db)
Kauffman polynomial	$- a z 9 - z 9 a -1 -3 a 2 z 8 -4 z 8 a -2 -7 z 8 -3 a 3 z 7 -8 a z 7 -11 z 7 a -1 -6 z 7 a -3 - a 4 z 6 + 4 a 2 z 6 -5 z 6 a -4 + 10 z 6 + 9 a 3 z 5 + 29 a z 5 + 31 z 5 a -1 + 8 z 5 a -3 -3 z 5 a -5 + 3 a 4 z 4 + 7 a 2 z 4 + 8 z 4 a -2 + 5 z 4 a -4 - z 4 a -6 + 6 z 4 -8 a 3 z 3 -28 a z 3 -30 z 3 a -1 -7 z 3 a -3 + 3 z 3 a -5 -3 a 4 z 2 -10 a 2 z 2 -6 z 2 a -2 -2 z 2 a -4 + z 2 a -6 -10 z 2 + 3 a 3 z + 13 a z + 14 z a -1 + 3 z a -3 - z a -5 + a 4 + 3 a 2 + 3- a 3 z -1 -3 a z -1 -2 a -1 z -1$ (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 L10a60. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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