L7a5

(Knotscape image)

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

Visit L7a5's page at the original Knot Atlas.

L7a5 is $7^2_2$ in the Rolfsen table of links.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$\frac{(u+v-1) (u v-u-v)}{u v}$ (db)
Jones polynomial	$-q^{3/2}+2 \sqrt{q}-\frac{3}{\sqrt{q}}+\frac{3}{q^{3/2}}-\frac{4}{q^{5/2}}+\frac{2}{q^{7/2}}-\frac{2}{q^{9/2}}+\frac{1}{q^{11/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- z a 5 + z 3 a 3 + z a 3 + a 3 z -1 + z 3 a - a z -1 - z a -1$ (db)
Kauffman polynomial	$- z 4 a 6 + 2 z 2 a 6 -2 z 5 a 5 + 5 z 3 a 5 -3 z a 5 - z 6 a 4 + 2 z 2 a 4 -4 z 5 a 3 + 8 z 3 a 3 -6 z a 3 + a 3 z -1 - z 6 a 2 - z 4 a 2 + 2 z 2 a 2 - a 2 -2 z 5 a + 2 z 3 a -2 z a + a z -1 -2 z 4 + 2 z 2 - z 3 a -1 + z a -1$ (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 L7a5. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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