L11a437

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_18,11,19,12 X_14,8,15,7 X_8,14,9,13 X_22,15,13,16 X_20,17,21,18 X_16,21,17,22 X_12,19,5,20 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -10, 2, -11}, {10, -1, 4, -5, 11, -2, 3, -9}, {5, -4, 6, -8, 7, -3, 9, -7, 8, -6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 3 + 2 u 3 + 5 v u 2 -3 v w u 2 + 3 w u 2 -5 u 2 -3 v u + 5 v w u -5 w u + 3 u -2 v w + 2 w$ (db)
Jones polynomial	$q -2 + 5 q -1 -7 q -2 + 11 q -3 -12 q -4 + 13 q -5 -10 q -6 + 9 q -7 -6 q -8 + 3 q -9 - q -10$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$- a 10 + 3 z 2 a 8 + 2 a 8 -2 z 4 a 6 -2 z 2 a 6 + a 6 z -2 -2 z 4 a 4 -2 z 2 a 4 -2 a 4 z -2 -3 a 4 - z 4 a 2 + a 2 z -2 + a 2 + z 2 + 1$ (db)
Kauffman polynomial	$z 7 a 11 -4 z 5 a 11 + 5 z 3 a 11 -2 z a 11 + 3 z 8 a 10 -12 z 6 a 10 + 14 z 4 a 10 -7 z 2 a 10 + 2 a 10 + 3 z 9 a 9 -8 z 7 a 9 -2 z 5 a 9 + 11 z 3 a 9 -4 z a 9 + z 10 a 8 + 5 z 8 a 8 -30 z 6 a 8 + 38 z 4 a 8 -18 z 2 a 8 + 4 a 8 + 6 z 9 a 7 -17 z 7 a 7 + 10 z 5 a 7 - z 3 a 7 + z 10 a 6 + 5 z 8 a 6 -21 z 6 a 6 + 19 z 4 a 6 -3 z 2 a 6 + a 6 z -2 -3 a 6 + 3 z 9 a 5 -5 z 7 a 5 + 6 z 5 a 5 -10 z 3 a 5 + 8 z a 5 -2 a 5 z -1 + 3 z 8 a 4 -9 z 4 a 4 + 13 z 2 a 4 + 2 a 4 z -2 -8 a 4 + 3 z 7 a 3 -5 z 3 a 3 + 6 z a 3 -2 a 3 z -1 + 3 z 6 a 2 -3 z 4 a 2 + 3 z 2 a 2 + a 2 z -2 -3 a 2 + 2 z 5 a -2 z 3 a + z 4 -2 z 2 + 1$ (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 =

-2 is the signature of L11a437. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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