L11a397

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$4 v u -3 v w u + 3 w u -3 u -3 v + 3 v w -4 w + 3$ (db)
Jones polynomial	$- q 7 + 3 q 6 -4 q 5 + 5 q 4 -7 q 3 + 8 q 2 -7 q + 7-4 q -1 + 4 q -2 - q -3 + q -4$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a 4 z -2 + a 4 -2 z 2 a 2 -2 a 2 z -2 -3 a 2 + z 4 + z 2 + z -2 + 2 + z 4 a -2 + z 4 a -4 + z 2 a -4 - z 2 a -6$ (db)
Kauffman polynomial	$z 10 a -2 + z 10 a -4 + z 9 a -1 + 4 z 9 a -3 + 3 z 9 a -5 -3 z 8 a -2 - z 8 a -4 + 3 z 8 a -6 + z 8 + a z 7 - z 7 a -1 -17 z 7 a -3 -14 z 7 a -5 + z 7 a -7 + a 2 z 6 + 5 z 6 a -2 -8 z 6 a -4 -14 z 6 a -6 + a 3 z 5 + a z 5 + 22 z 5 a -3 + 18 z 5 a -5 -4 z 5 a -7 + a 4 z 4 + 2 a 2 z 4 -6 z 4 a -2 + 10 z 4 a -4 + 16 z 4 a -6 + z 4 -10 z 3 a -3 -7 z 3 a -5 + 3 z 3 a -7 -3 a 4 z 2 -6 a 2 z 2 + z 2 a -2 -2 z 2 a -4 -3 z 2 a -6 -3 z 2 -3 a 3 z -3 a z + 3 a 4 + 5 a 2 + 3 + 2 a 3 z -1 + 2 a z -1 - a 4 z -2 -2 a 2 z -2 - z -2$ (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 L11a397. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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