L7n1

(Knotscape image)

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

Visit L7n1's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_12,7,13,8 X_4,13,1,14 X_5,10,6,11 X₃₈₄₉ X_9,14,10,5 X_11,2,12,3
Gauss code	{1, 7, -5, -3}, {-4, -1, 2, 5, -6, 4, -7, -2, 3, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 3 -1$ (db)
Jones polynomial	$-\frac{1}{q^{5/2}}-\frac{1}{q^{9/2}}-\frac{1}{q^{13/2}}+\frac{1}{q^{15/2}}$ (db)
Signature	-5 (db)
HOMFLY-PT polynomial	$- a 9 z -1 + z 3 a 7 + 4 z a 7 + 3 a 7 z -1 - z 5 a 5 -5 z 3 a 5 -6 z a 5 -2 a 5 z -1$ (db)
Kauffman polynomial	$- a 10 - z a 9 + a 9 z -1 - z 4 a 8 + 4 z 2 a 8 -3 a 8 - z 5 a 7 + 5 z 3 a 7 -7 z a 7 + 3 a 7 z -1 - z 4 a 6 + 4 z 2 a 6 -3 a 6 - z 5 a 5 + 5 z 3 a 5 -6 z a 5 + 2 a 5 z -1$ (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 =

-5 is the signature of L7n1. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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