L11n147

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_18,9,19,10 X₆₇₁₈ X_22,19,7,20 X_5,13,6,12 X_3,10,4,11 X_15,5,16,4 X_11,16,12,17 X_20,13,21,14 X_14,21,15,22 X_17,2,18,3
Gauss code	{1, 11, -6, 7, -5, -3}, {3, -1, 2, 6, -8, 5, 9, -10, -7, 8, -11, -2, 4, -9, 10, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + v u 4 + 2 v 2 u 3 - v u 3 + u 3 -2 v 2 u 2 + v u 2 -2 u 2 + v 2 u - v u + 2 u + v -1$ (db)
Jones polynomial	$-\frac{1}{\sqrt{q}}+\frac{2}{q^{3/2}}-\frac{4}{q^{5/2}}+\frac{4}{q^{7/2}}-\frac{6}{q^{9/2}}+\frac{5}{q^{11/2}}-\frac{5}{q^{13/2}}+\frac{4}{q^{15/2}}-\frac{2}{q^{17/2}}+\frac{1}{q^{19/2}}$ (db)
Signature	-5 (db)
HOMFLY-PT polynomial	$- a 9 z -1 - z 5 a 7 -3 z 3 a 7 + 2 a 7 z -1 + z 7 a 5 + 5 z 5 a 5 + 7 z 3 a 5 + 3 z a 5 - z 5 a 3 -4 z 3 a 3 -4 z a 3 - a 3 z -1$ (db)
Kauffman polynomial	$- z 2 a 12 -2 z 3 a 11 -4 z 4 a 10 + 5 z 2 a 10 -2 a 10 - z 7 a 9 + 3 z 3 a 9 -2 z a 9 + a 9 z -1 -2 z 8 a 8 + 7 z 6 a 8 -11 z 4 a 8 + 13 z 2 a 8 -5 a 8 - z 9 a 7 + z 7 a 7 + 5 z 5 a 7 -3 z 3 a 7 -2 z a 7 + 2 a 7 z -1 -4 z 8 a 6 + 16 z 6 a 6 -17 z 4 a 6 + 8 z 2 a 6 -3 a 6 - z 9 a 5 + z 7 a 5 + 10 z 5 a 5 -16 z 3 a 5 + 5 z a 5 -2 z 8 a 4 + 9 z 6 a 4 -10 z 4 a 4 + z 2 a 4 + a 4 - z 7 a 3 + 5 z 5 a 3 -8 z 3 a 3 + 5 z a 3 - a 3 z -1$ (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 =

-5 is the signature of L11n147. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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