L7a6

(Knotscape image)

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

Visit L7a6's page at the original Knot Atlas.

Planar diagram presentation	X₈₁₉₂ X_10,4,11,3 X_14,10,7,9 X_12,6,13,5 X₂₇₃₈ X_4,12,5,11 X_6,14,1,13
Gauss code	{1, -5, 2, -6, 4, -7}, {5, -1, 3, -2, 6, -4, 7, -3}

A Braid Representative

A Morse Link Presentation

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

3 is the signature of L7a6. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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