L10n105

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_5,12,6,13 X₃₈₄₉ X_2,16,3,15 X_7,17,8,16 X_14,9,11,10 X_20,13,15,14 X_19,5,20,10 X_11,18,12,19 X_17,1,18,4
Gauss code	{1, -4, -3, 10}, {-9, 2, 7, -6}, {-2, -1, -5, 3, 6, 8}, {4, 5, -10, 9, -8, -7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v w u 2 + v 2 u - v u + v w u + v x u - v w x u + w x u - v x$ (db)
Jones polynomial	$-2 q^{3/2}+\sqrt{q}-\frac{4}{\sqrt{q}}+\frac{2}{q^{3/2}}-\frac{4}{q^{5/2}}+\frac{1}{q^{7/2}}-\frac{2}{q^{9/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$2 a 5 z -1 + a 5 z -3 -4 z a 3 -7 a 3 z -1 -3 a 3 z -3 + 2 z 3 a + 6 z a + 8 a z -1 + 3 a z -3 -2 z a -1 -3 a -1 z -1 - a -1 z -3$ (db)
Kauffman polynomial	$- a 3 z 7 - a z 7 - a 4 z 6 -2 a 2 z 6 - z 6 + 5 a 3 z 5 + 5 a z 5 + 4 a 4 z 4 + 8 a 2 z 4 + 4 z 4 -3 a 5 z 3 -15 a 3 z 3 -15 a z 3 -3 z 3 a -1 -10 a 4 z 2 -20 a 2 z 2 -10 z 2 + 8 a 5 z + 19 a 3 z + 19 a z + 8 z a -1 + 10 a 4 + 19 a 2 + 10-5 a 5 z -1 -12 a 3 z -1 -12 a z -1 -5 a -1 z -1 -3 a 4 z -2 -6 a 2 z -2 -3 z -2 + a 5 z -3 + 3 a 3 z -3 + 3 a z -3 + a -1 z -3$ (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 =

-1 is the signature of L10n105. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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