L11n276

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_5,12,6,13 X₃₈₄₉ X_13,2,14,3 X_14,7,15,8 X_9,18,10,19 X_22,17,11,18 X_20,11,21,12 X_16,21,17,22 X_4,15,1,16 X_19,10,20,5
Gauss code	{1, 4, -3, -10}, {-2, -1, 5, 3, -6, 11}, {8, 2, -4, -5, 10, -9, 7, 6, -11, -8, 9, -7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 w u 4 + v w u 3 + v u 2 - v w u 2 - v u + 1$ (db)
Jones polynomial	$q -4 + q -6 + q -7 + 2 q -9 - q -10 + q -11 - q -12$ (db)
Signature	-6 (db)
HOMFLY-PT polynomial	$- a 14 z -2 + 2 z 2 a 12 + 4 a 12 z -2 + 6 a 12 - z 6 a 10 -8 z 4 a 10 -19 z 2 a 10 -5 a 10 z -2 -16 a 10 + z 8 a 8 + 8 z 6 a 8 + 21 z 4 a 8 + 22 z 2 a 8 + 2 a 8 z -2 + 10 a 8$ (db)
Kauffman polynomial	$z 3 a 15 -2 z a 15 + a 15 z -1 + z 4 a 14 -2 z 2 a 14 - a 14 z -2 + 2 a 14 - z 5 a 13 + 8 z 3 a 13 -13 z a 13 + 5 a 13 z -1 - z 6 a 12 + 7 z 4 a 12 -14 z 2 a 12 -4 a 12 z -2 + 13 a 12 + z 7 a 11 -9 z 5 a 11 + 26 z 3 a 11 -27 z a 11 + 9 a 11 z -1 + z 8 a 10 -9 z 6 a 10 + 27 z 4 a 10 -34 z 2 a 10 -5 a 10 z -2 + 20 a 10 + z 7 a 9 -8 z 5 a 9 + 19 z 3 a 9 -16 z a 9 + 5 a 9 z -1 + z 8 a 8 -8 z 6 a 8 + 21 z 4 a 8 -22 z 2 a 8 -2 a 8 z -2 + 10 a 8$ (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 =

-6 is the signature of L11n276. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -9$	$i = -7$	$i = -5$
$r = -9$		${\mathbb Z}$
$r = -8$		${\mathbb Z}_2$	${\mathbb Z}$
$r = -7$		${\mathbb Z}$
$r = -6$		${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}^{3}$
$r = -5$	${\mathbb Z}$	${\mathbb Z}$
$r = -4$		${\mathbb Z}^{2}$	${\mathbb Z}^{2}$
$r = -3$	${\mathbb Z}$
$r = -2$	${\mathbb Z}_2$	${\mathbb Z}$
$r = -1$
$r = 0$	${\mathbb Z}$	${\mathbb Z}$