L6a2

(Knotscape image)

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

Visit L6a2's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_12,5,7,6 X_10,3,11,4 X_4,11,5,12 X₂₇₃₈ X_6,9,1,10
Gauss code	{1, -5, 3, -4, 2, -6}, {5, -1, 6, -3, 4, -2}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 2 - v 2 u + v u - u - v$ (db)
Jones polynomial	$-\frac{1}{q^{3/2}}+\frac{1}{q^{5/2}}-\frac{2}{q^{7/2}}+\frac{2}{q^{9/2}}-\frac{2}{q^{11/2}}+\frac{1}{q^{13/2}}-\frac{1}{q^{15/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$z a 7 + a 7 z -1 - z 3 a 5 -2 z a 5 - a 5 z -1 - z 3 a 3 -2 z a 3$ (db)
Kauffman polynomial	$- z 3 a 9 + 2 z a 9 - z 4 a 8 + z 2 a 8 - z 5 a 7 + 2 z 3 a 7 -3 z a 7 + a 7 z -1 -2 z 4 a 6 + 2 z 2 a 6 - a 6 - z 5 a 5 + 2 z 3 a 5 -3 z a 5 + a 5 z -1 - z 4 a 4 + z 2 a 4 - z 3 a 3 + 2 z a 3$ (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 L6a2. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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