L11n296

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,4,13,3 X_15,20,16,21 X_14,8,15,7 X_10,22,5,21 X_18,11,19,12 X_9,17,10,16 X_22,17,11,18 X_19,9,20,8 X₂₅₃₆ X_4,14,1,13
Gauss code	{1, -10, 2, -11}, {10, -1, 4, 9, -7, -5}, {6, -2, 11, -4, -3, 7, 8, -6, -9, 3, 5, -8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 4 - v w u 4 + w u 4 -2 v u 3 + v w u 3 - w u 3 + u 3 + v u 2 - v w u 2 + v 2 u - v u - v 2 w u + 2 v w u - v 2 + v - v w$ (db)
Jones polynomial	$q 6 -2 q 5 + 4 q 4 -4 q 3 + 7 q 2 -5 q + 6-4 q -1 + 2 q -2 - q -3$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$- z 6 a -2 -5 z 4 a -2 + z 4 a -4 + 2 z 4 - a 2 z 2 -10 z 2 a -2 + 3 z 2 a -4 + 7 z 2 -2 a 2 -10 a -2 + 3 a -4 + 9- a 2 z -2 -5 a -2 z -2 + 2 a -4 z -2 + 4 z -2$ (db)
Kauffman polynomial	$z 9 a -1 + z 9 a -3 + 5 z 8 a -2 + 3 z 8 a -4 + 2 z 8 + a z 7 - z 7 a -1 + 2 z 7 a -5 -25 z 6 a -2 -14 z 6 a -4 + z 6 a -6 -10 z 6 -4 a z 5 -10 z 5 a -1 -13 z 5 a -3 -7 z 5 a -5 + 2 a 2 z 4 + 48 z 4 a -2 + 23 z 4 a -4 -4 z 4 a -6 + 23 z 4 + a 3 z 3 + 12 a z 3 + 30 z 3 a -1 + 23 z 3 a -3 + 4 z 3 a -5 -3 a 2 z 2 -44 z 2 a -2 -22 z 2 a -4 + 3 z 2 a -6 -22 z 2 -2 a 3 z -13 a z -27 z a -1 -16 z a -3 + 2 a 2 + 20 a -2 + 10 a -4 + 13 + a 3 z -1 + 5 a z -1 + 9 a -1 z -1 + 5 a -3 z -1 - a 2 z -2 -5 a -2 z -2 -2 a -4 z -2 -4 z -2$ (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 =

0 is the signature of L11n296. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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