L7a2

(Knotscape image)

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

Visit L7a2's page at the original Knot Atlas.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- u 3 -2 v u 2 + 2 u 2 + 2 v u -2 u - v$ (db)
Jones polynomial	$-\frac{1}{q^{3/2}}+\frac{2}{q^{5/2}}-\frac{4}{q^{7/2}}+\frac{3}{q^{9/2}}-\frac{4}{q^{11/2}}+\frac{3}{q^{13/2}}-\frac{2}{q^{15/2}}+\frac{1}{q^{17/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- a 9 z -1 + 3 z a 7 + 3 a 7 z -1 -2 z 3 a 5 -4 z a 5 -2 a 5 z -1 - z 3 a 3 - z a 3$ (db)
Kauffman polynomial	$- z 4 a 10 + 2 z 2 a 10 - a 10 -2 z 5 a 9 + 4 z 3 a 9 -2 z a 9 + a 9 z -1 - z 6 a 8 -2 z 4 a 8 + 7 z 2 a 8 -3 a 8 -5 z 5 a 7 + 10 z 3 a 7 -8 z a 7 + 3 a 7 z -1 - z 6 a 6 -3 z 4 a 6 + 6 z 2 a 6 -3 a 6 -3 z 5 a 5 + 5 z 3 a 5 -5 z a 5 + 2 a 5 z -1 -2 z 4 a 4 + z 2 a 4 - z 3 a 3 + z a 3$ (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 L7a2. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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