L11a454

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 3 + 3 v u 3 + v 2 w u 3 -2 v w u 3 + w u 3 - u 3 - v 3 u 2 + 7 v 2 u 2 -6 v u 2 -4 v 2 w u 2 + 6 v w u 2 -2 w u 2 + u 2 + 2 v 3 u -6 v 2 u + 4 v u - v 3 w u + 6 v 2 w u -7 v w u + w u - v 3 + 2 v 2 - v + v 3 w -3 v 2 w + 2 v w$ (db)
Jones polynomial	$- q 5 + 4 q 4 -10 q 3 + 17 q 2 -21 q + 25-23 q -1 + 21 q -2 -14 q -3 + 8 q -4 -3 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a 6 -3 z 2 a 4 + a 4 z -2 - a 4 + 3 z 4 a 2 + z 2 a 2 -2 a 2 z -2 -3 a 2 - z 6 + 2 z 2 + z -2 + 4 + 2 z 4 a -2 - a -2 - z 2 a -4$ (db)
Kauffman polynomial	$2 a 2 z 10 + 2 z 10 + 5 a 3 z 9 + 13 a z 9 + 8 z 9 a -1 + 5 a 4 z 8 + 13 a 2 z 8 + 12 z 8 a -2 + 20 z 8 + 3 a 5 z 7 -3 a 3 z 7 -16 a z 7 - z 7 a -1 + 9 z 7 a -3 + a 6 z 6 -9 a 4 z 6 -39 a 2 z 6 -20 z 6 a -2 + 4 z 6 a -4 -53 z 6 -7 a 5 z 5 -10 a 3 z 5 -8 a z 5 -19 z 5 a -1 -13 z 5 a -3 + z 5 a -5 -3 a 6 z 4 + 5 a 4 z 4 + 41 a 2 z 4 + 16 z 4 a -2 -4 z 4 a -4 + 53 z 4 + 5 a 5 z 3 + 14 a 3 z 3 + 19 a z 3 + 19 z 3 a -1 + 8 z 3 a -3 - z 3 a -5 + 3 a 6 z 2 -3 a 4 z 2 -27 a 2 z 2 -10 z 2 a -2 + z 2 a -4 -32 z 2 - a 5 z -8 a 3 z -12 a z -7 z a -1 -2 z a -3 - a 6 + 3 a 4 + 11 a 2 + 3 a -2 + 11 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 L11a454. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{3}$
$r = -3$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -2$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = 0$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{14}$
$r = 1$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 2$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$