L10a63

(Knotscape image)

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

Visit L10a63's page at the original Knot Atlas.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + 2 v u 4 - u 4 + 2 v 2 u 3 -5 v u 3 + 2 u 3 -2 v 2 u 2 + 5 v u 2 -2 u 2 + 2 v 2 u -5 v u + 2 u - v 2 + 2 v -1$ (db)
Jones polynomial	$q^{3/2}-3 \sqrt{q}+\frac{5}{\sqrt{q}}-\frac{9}{q^{3/2}}+\frac{10}{q^{5/2}}-\frac{12}{q^{7/2}}+\frac{11}{q^{9/2}}-\frac{9}{q^{11/2}}+\frac{6}{q^{13/2}}-\frac{3}{q^{15/2}}+\frac{1}{q^{17/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- z 3 a 7 -2 z a 7 - a 7 z -1 + 2 z 5 a 5 + 7 z 3 a 5 + 8 z a 5 + 3 a 5 z -1 - z 7 a 3 -5 z 5 a 3 -10 z 3 a 3 -9 z a 3 -2 a 3 z -1 + z 5 a + 3 z 3 a + 2 z a$ (db)
Kauffman polynomial	$- z 4 a 10 + z 2 a 10 -3 z 5 a 9 + 3 z 3 a 9 -5 z 6 a 8 + 6 z 4 a 8 -3 z 2 a 8 + a 8 -6 z 7 a 7 + 10 z 5 a 7 -10 z 3 a 7 + 5 z a 7 - a 7 z -1 -4 z 8 a 6 + 2 z 6 a 6 + 6 z 4 a 6 -9 z 2 a 6 + 3 a 6 - z 9 a 5 -10 z 7 a 5 + 32 z 5 a 5 -35 z 3 a 5 + 16 z a 5 -3 a 5 z -1 -7 z 8 a 4 + 14 z 6 a 4 -3 z 4 a 4 -6 z 2 a 4 + 3 a 4 - z 9 a 3 -7 z 7 a 3 + 29 z 5 a 3 -32 z 3 a 3 + 15 z a 3 -2 a 3 z -1 -3 z 8 a 2 + 6 z 6 a 2 + z 4 a 2 -3 z 2 a 2 -3 z 7 a + 10 z 5 a -10 z 3 a + 4 z a - z 6 + 3 z 4 -2 z 2$ (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 =

-3 is the signature of L10a63. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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