L7a7

(Knotscape image)

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

Visit L7a7's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_14,12,9,11 X_8,14,5,13 X_12,8,13,7 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -6, 2, -7}, {6, -1, 5, -4}, {7, -2, 3, -5, 4, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u - v w u + w u - u - v + v w -2 w + 1$ (db)
Jones polynomial	$- q 3 + 3 q 2 -3 q + 4-3 q -1 + 4 q -2 - q -3 + q -4$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a 4 z -2 + a 4 -2 z 2 a 2 -2 a 2 z -2 -3 a 2 + z 4 + 2 z 2 + z -2 + 2- z 2 a -2$ (db)
Kauffman polynomial	$a 2 z 6 + z 6 + a 3 z 5 + 4 a z 5 + 3 z 5 a -1 + a 4 z 4 + a 2 z 4 + 3 z 4 a -2 + 3 z 4 -4 a z 3 -3 z 3 a -1 + z 3 a -3 -3 a 4 z 2 -5 a 2 z 2 -3 z 2 a -2 -5 z 2 -3 a 3 z -3 a z + 3 a 4 + 5 a 2 + 3 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 =

0 is the signature of L7a7. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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