L11n145

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_18,11,19,12 X_10,4,11,3 X_2,17,3,18 X_12,5,13,6 X₆₇₁₈ X_16,10,17,9 X_15,20,16,21 X_13,22,14,7 X_21,14,22,15 X_4,20,5,19
Gauss code	{1, -4, 3, -11, 5, -6}, {6, -1, 7, -3, 2, -5, -9, 10, -8, -7, 4, -2, 11, 8, -10, 9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + v u 4 + 3 v 2 u 3 -4 v u 3 + u 3 -3 v 2 u 2 + 5 v u 2 -3 u 2 + v 2 u -4 v u + 3 u + v -1$ (db)
Jones polynomial	$q^{3/2}-4 \sqrt{q}+\frac{6}{\sqrt{q}}-\frac{9}{q^{3/2}}+\frac{10}{q^{5/2}}-\frac{11}{q^{7/2}}+\frac{9}{q^{9/2}}-\frac{7}{q^{11/2}}+\frac{4}{q^{13/2}}-\frac{1}{q^{15/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$- a 3 z 7 + a 5 z 5 -4 a 3 z 5 + a z 5 + 2 a 5 z 3 -4 a 3 z 3 + 2 a z 3 - a z + a 3 z -1 - a z -1$ (db)
Kauffman polynomial	$- z 3 a 9 -4 z 4 a 8 + 2 z 2 a 8 - z 7 a 7 -3 z 5 a 7 + 2 z 3 a 7 -3 z 8 a 6 + 7 z 6 a 6 -12 z 4 a 6 + 6 z 2 a 6 -2 z 9 a 5 + 2 z 7 a 5 -8 z 8 a 4 + 23 z 6 a 4 -20 z 4 a 4 + 6 z 2 a 4 -2 z 9 a 3 - z 7 a 3 + 15 z 5 a 3 -10 z 3 a 3 - z a 3 + a 3 z -1 -5 z 8 a 2 + 15 z 6 a 2 -10 z 4 a 2 + 2 z 2 a 2 - a 2 -4 z 7 a + 12 z 5 a -7 z 3 a - z a + a z -1 - z 6 + 2 z 4$ (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 L11n145. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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