L11a395

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u 3 - v w u 3 + 2 w u 3 -2 u 3 -5 v u 2 + 4 v w u 2 -5 w u 2 + 4 u 2 + 5 v u -4 v w u + 5 w u -4 u -2 v + 2 v w -2 w + 1$ (db)
Jones polynomial	$1-4 q -1 + 8 q -2 -11 q -3 + 15 q -4 -15 q -5 + 17 q -6 -12 q -7 + 9 q -8 -5 q -9 + 2 q -10 - q -11$ (db)
Signature	-4 (db)
HOMFLY-PT polynomial	$- a 12 z -2 + 4 a 10 z -2 + 4 a 10 -6 z 2 a 8 -5 a 8 z -2 -11 a 8 + 4 z 4 a 6 + 9 z 2 a 6 + 2 a 6 z -2 + 7 a 6 - z 6 a 4 -2 z 4 a 4 - z 2 a 4 + z 4 a 2 + z 2 a 2$ (db)
Kauffman polynomial	$z 5 a 13 -3 z 3 a 13 + 3 z a 13 - a 13 z -1 + 2 z 6 a 12 -4 z 4 a 12 + 3 z 2 a 12 + a 12 z -2 -2 a 12 + 2 z 7 a 11 + 2 z 5 a 11 -12 z 3 a 11 + 13 z a 11 -5 a 11 z -1 + 2 z 8 a 10 + 4 z 6 a 10 -13 z 4 a 10 + 14 z 2 a 10 + 4 a 10 z -2 -10 a 10 + 2 z 9 a 9 + z 7 a 9 + 3 z 5 a 9 -16 z 3 a 9 + 21 z a 9 -9 a 9 z -1 + z 10 a 8 + 4 z 8 a 8 -4 z 6 a 8 -8 z 4 a 8 + 20 z 2 a 8 + 5 a 8 z -2 -14 a 8 + 6 z 9 a 7 -9 z 7 a 7 + 4 z 5 a 7 -6 z 3 a 7 + 11 z a 7 -5 a 7 z -1 + z 10 a 6 + 8 z 8 a 6 -22 z 6 a 6 + 11 z 4 a 6 + 6 z 2 a 6 + 2 a 6 z -2 -7 a 6 + 4 z 9 a 5 -4 z 7 a 5 -8 z 5 a 5 + 6 z 3 a 5 + 6 z 8 a 4 -15 z 6 a 4 + 8 z 4 a 4 -2 z 2 a 4 + 4 z 7 a 3 -10 z 5 a 3 + 5 z 3 a 3 + z 6 a 2 -2 z 4 a 2 + z 2 a 2$ (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 =

-4 is the signature of L11a395. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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