L11a466

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u 3 -2 v w u 3 + w u 3 - u 3 -6 v u 2 + 6 v w u 2 -5 w u 2 + 5 u 2 + 5 v u -5 v w u + 6 w u -6 u - v + v w -2 w + 2$ (db)
Jones polynomial	$- q 2 + 3 q -6 + 12 q -1 -15 q -2 + 19 q -3 -17 q -4 + 16 q -5 -12 q -6 + 7 q -7 -3 q -8 + q -9$ (db)
Signature	-2 (db)
HOMFLY-PT polynomial	$z 2 a 8 + a 8 -2 z 4 a 6 -3 z 2 a 6 + a 6 z -2 - a 6 + z 6 a 4 + z 4 a 4 -2 z 2 a 4 -2 a 4 z -2 -4 a 4 + z 6 a 2 + 3 z 4 a 2 + 6 z 2 a 2 + a 2 z -2 + 5 a 2 - z 4 -2 z 2 -1$ (db)
Kauffman polynomial	$z 6 a 10 -3 z 4 a 10 + 3 z 2 a 10 - a 10 + 3 z 7 a 9 -8 z 5 a 9 + 7 z 3 a 9 -2 z a 9 + 4 z 8 a 8 -6 z 6 a 8 -3 z 4 a 8 + 6 z 2 a 8 - a 8 + 3 z 9 a 7 + 2 z 7 a 7 -17 z 5 a 7 + 15 z 3 a 7 -6 z a 7 + z 10 a 6 + 8 z 8 a 6 -15 z 6 a 6 + 6 z 2 a 6 + a 6 z -2 -3 a 6 + 6 z 9 a 5 - z 7 a 5 -15 z 5 a 5 + 12 z 3 a 5 - z a 5 -2 a 5 z -1 + z 10 a 4 + 8 z 8 a 4 -9 z 6 a 4 -9 z 4 a 4 + 16 z 2 a 4 + 2 a 4 z -2 -8 a 4 + 3 z 9 a 3 + 4 z 7 a 3 -10 z 5 a 3 + 3 z 3 a 3 + 5 z a 3 -2 a 3 z -1 + 4 z 8 a 2 + 2 z 6 a 2 -15 z 4 a 2 + 18 z 2 a 2 + a 2 z -2 -8 a 2 + 4 z 7 a -3 z 5 a -3 z 3 a + 3 z a + 3 z 6 -6 z 4 + 5 z 2 -2 + z 5 a -1 -2 z 3 a -1 + z a -1$ (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 L11a466. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -3$	$i = -1$
$r = -8$	${\mathbb Z}$
$r = -7$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -5$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -4$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{9}$
$r = -3$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = -2$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = -1$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 0$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{8}$
$r = 1$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 2$	${\mathbb Z}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 3$	${\mathbb Z}_2$	${\mathbb Z}$