L11n435

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_14,4,15,3 X_12,14,7,13 X₂₇₃₈ X_22,10,13,9 X_6,22,1,21 X_20,16,21,15 X_16,5,17,6 X_11,19,12,18 X_17,11,18,10 X_4,19,5,20
Gauss code	{1, -4, 2, -11, 8, -6}, {4, -1, 5, 10, -9, -3}, {3, -2, 7, -8, -10, 9, 11, -7, 6, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 3 + v u 3 + v 2 w u 3 -2 v w u 3 + w u 3 + 2 v 2 u 2 -2 v w 2 u 2 + w 2 u 2 -2 v u 2 -2 v 2 w u 2 + 5 v w u 2 -2 w u 2 - v 2 u + 2 v w 2 u -2 w 2 u + 2 v u + 2 v 2 w u -5 v w u + 2 w u - v w 2 + w 2 - v 2 w + 2 v w - w$ (db)
Jones polynomial	$- q 8 + 4 q 7 -8 q 6 + 12 q 5 -14 q 4 + 16 q 3 -13 q 2 + 11 q -6 + 3 q -1$ (db)
Signature	2 (db)
HOMFLY-PT polynomial	$z 6 a -4 -4 z 4 a -2 + 3 z 4 a -4 - z 4 a -6 -10 z 2 a -2 + 6 z 2 a -4 - z 2 a -6 + 3 z 2 -8 a -2 + 5 a -4 - a -6 + 4-2 a -2 z -2 + a -4 z -2 + z -2$ (db)
Kauffman polynomial	$3 z 9 a -3 + 3 z 9 a -5 + 6 z 8 a -2 + 13 z 8 a -4 + 7 z 8 a -6 + 3 z 7 a -1 + 4 z 7 a -5 + 7 z 7 a -7 -18 z 6 a -2 -34 z 6 a -4 -12 z 6 a -6 + 4 z 6 a -8 -3 z 5 a -1 -7 z 5 a -3 -17 z 5 a -5 -12 z 5 a -7 + z 5 a -9 + 34 z 4 a -2 + 41 z 4 a -4 + 7 z 4 a -6 -6 z 4 a -8 + 6 z 4 + 3 z 3 a -1 + 12 z 3 a -3 + 14 z 3 a -5 + 4 z 3 a -7 - z 3 a -9 -31 z 2 a -2 -24 z 2 a -4 -4 z 2 a -6 + z 2 a -8 -12 z 2 -6 z a -1 -8 z a -3 -3 z a -5 - z a -7 + 12 a -2 + 8 a -4 + a -6 + 6 + 2 a -1 z -1 + 2 a -3 z -1 -2 a -2 z -2 - a -4 z -2 - z -2$ (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 =

2 is the signature of L11n435. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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