L11a467

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v u 4 - u 4 + 2 v 2 u 3 -6 v u 3 - v 2 w u 3 + 3 v w u 3 -2 w u 3 + 3 u 3 -4 v 2 u 2 + 8 v u 2 + 3 v 2 w u 2 -8 v w u 2 + 4 w u 2 -3 u 2 + 2 v 2 u -3 v u -3 v 2 w u + 6 v w u -2 w u + u + v 2 w - v w$ (db)
Jones polynomial	$- q 5 + 4 q 4 -9 q 3 + 15 q 2 -19 q + 23-21 q -1 + 19 q -2 -13 q -3 + 8 q -4 -3 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a 6 -3 z 2 a 4 + a 4 z -2 - a 4 + 3 z 4 a 2 + 2 z 2 a 2 -2 a 2 z -2 -2 a 2 - z 6 - z 4 - z 2 + z -2 + 2 + 2 z 4 a -2 + z 2 a -2 - z 2 a -4$ (db)
Kauffman polynomial	$a 2 z 10 + z 10 + 4 a 3 z 9 + 9 a z 9 + 5 z 9 a -1 + 5 a 4 z 8 + 16 a 2 z 8 + 9 z 8 a -2 + 20 z 8 + 3 a 5 z 7 + a 3 z 7 - a z 7 + 9 z 7 a -1 + 8 z 7 a -3 + a 6 z 6 -10 a 4 z 6 -44 a 2 z 6 -11 z 6 a -2 + 4 z 6 a -4 -48 z 6 -7 a 5 z 5 -18 a 3 z 5 -31 a z 5 -33 z 5 a -1 -12 z 5 a -3 + z 5 a -5 -3 a 6 z 4 + 7 a 4 z 4 + 46 a 2 z 4 + 5 z 4 a -2 -5 z 4 a -4 + 46 z 4 + 5 a 5 z 3 + 20 a 3 z 3 + 34 a z 3 + 27 z 3 a -1 + 7 z 3 a -3 - z 3 a -5 + 3 a 6 z 2 -5 a 4 z 2 -30 a 2 z 2 -4 z 2 a -2 + 2 z 2 a -4 -28 z 2 - a 5 z -10 a 3 z -14 a z -7 z a -1 -2 z a -3 - a 6 + 4 a 4 + 12 a 2 + 2 a -2 + 10 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 L11a467. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{3}$
$r = -3$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{9}$
$r = -1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 0$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{12}$
$r = 1$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 2$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{9}$
$r = 3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$