L11a449

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$v 3 u 3 - v 2 u 3 - v 3 w u 3 + 2 v 2 w u 3 - v w u 3 -2 v 3 u 2 + 4 v 2 u 2 -2 v u 2 + v 3 w u 2 -4 v 2 w u 2 + 5 v w u 2 - w u 2 + v 3 u -5 v 2 u + 4 v u + 2 v 2 w u -4 v w u + 2 w u - u + v 2 -2 v + v w - w + 1$ (db)
Jones polynomial	$- q 5 + 3 q 4 -6 q 3 + 10 q 2 -13 q + 17-15 q -1 + 14 q -2 -10 q -3 + 7 q -4 -3 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$z 8 -2 a 2 z 6 - z 6 a -2 + 6 z 6 + a 4 z 4 -9 a 2 z 4 -4 z 4 a -2 + 14 z 4 + 3 a 4 z 2 -14 a 2 z 2 -5 z 2 a -2 + 15 z 2 + 3 a 4 -9 a 2 -2 a -2 + 8 + a 4 z -2 -2 a 2 z -2 + z -2$ (db)
Kauffman polynomial	$a 2 z 10 + z 10 + 3 a 3 z 9 + 7 a z 9 + 4 z 9 a -1 + 4 a 4 z 8 + 8 a 2 z 8 + 6 z 8 a -2 + 10 z 8 + 3 a 5 z 7 - a 3 z 7 -14 a z 7 -5 z 7 a -1 + 5 z 7 a -3 + a 6 z 6 -8 a 4 z 6 -30 a 2 z 6 -16 z 6 a -2 + 3 z 6 a -4 -40 z 6 -8 a 5 z 5 -13 a 3 z 5 + 3 a z 5 -4 z 5 a -1 -11 z 5 a -3 + z 5 a -5 -3 a 6 z 4 + a 4 z 4 + 39 a 2 z 4 + 21 z 4 a -2 -6 z 4 a -4 + 62 z 4 + 5 a 5 z 3 + 14 a 3 z 3 + 16 a z 3 + 16 z 3 a -1 + 7 z 3 a -3 -2 z 3 a -5 + 3 a 6 z 2 -2 a 4 z 2 -28 a 2 z 2 -13 z 2 a -2 + z 2 a -4 -37 z 2 - a 5 z -8 a 3 z -12 a z -7 z a -1 -2 z a -3 - a 6 + 3 a 4 + 11 a 2 + 3 a -2 + 11 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 L11a449. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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