L10a71

(Knotscape image)

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

Visit L10a71's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_18,9,19,10 X_14,6,15,5 X_16,8,17,7 X_10,4,11,3 X_20,12,7,11 X_12,15,13,16 X_6,14,1,13 X_4,19,5,20 X_2,18,3,17
Gauss code	{1, -10, 5, -9, 3, -8}, {4, -1, 2, -5, 6, -7, 8, -3, 7, -4, 10, -2, 9, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + 2 v u 4 - u 4 + 4 v 2 u 3 -7 v u 3 + 3 u 3 -5 v 2 u 2 + 11 v u 2 -5 u 2 + 3 v 2 u -7 v u + 4 u - v 2 + 2 v -1$ (db)
Jones polynomial	$-q^{13/2}+4 q^{11/2}-9 q^{9/2}+14 q^{7/2}-18 q^{5/2}+19 q^{3/2}-19 \sqrt{q}+\frac{14}{\sqrt{q}}-\frac{10}{q^{3/2}}+\frac{5}{q^{5/2}}-\frac{1}{q^{7/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 7 a -1 + a z 5 -3 z 5 a -1 + 2 z 5 a -3 + a z 3 -2 z 3 a -1 + 4 z 3 a -3 - z 3 a -5 - a z + 2 z a -1 + z a -3 - z a -5 + a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$-3 z 9 a -1 -3 z 9 a -3 -17 z 8 a -2 -8 z 8 a -4 -9 z 8 -10 a z 7 -17 z 7 a -1 -15 z 7 a -3 -8 z 7 a -5 -5 a 2 z 6 + 25 z 6 a -2 + 8 z 6 a -4 -4 z 6 a -6 + 8 z 6 - a 3 z 5 + 16 a z 5 + 42 z 5 a -1 + 39 z 5 a -3 + 13 z 5 a -5 - z 5 a -7 + 5 a 2 z 4 -4 z 4 a -2 + z 4 a -4 + 5 z 4 a -6 + 5 z 4 -6 a z 3 -22 z 3 a -1 -26 z 3 a -3 -9 z 3 a -5 + z 3 a -7 -2 z 2 a -2 -2 z 2 a -4 -2 z 2 a -6 -2 z 2 - a z + 4 z a -3 + 3 z a -5 - a -2 + a -1 z -1 + a -3 z -1$ (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 L10a71. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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