L11a210

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_20,9,21,10 X₆₇₁₈ X_22,15,7,16 X_4,14,5,13 X_16,6,17,5 X_12,18,13,17 X_10,4,11,3 X_18,12,19,11 X_14,21,15,22 X_2,20,3,19
Gauss code	{1, -11, 8, -5, 6, -3}, {3, -1, 2, -8, 9, -7, 5, -10, 4, -6, 7, -9, 11, -2, 10, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 4 + 3 v u 4 - u 4 + 5 v 2 u 3 -9 v u 3 + 4 u 3 -6 v 2 u 2 + 11 v u 2 -6 u 2 + 4 v 2 u -9 v u + 5 u - v 2 + 3 v -2$ (db)
Jones polynomial	$-q^{11/2}+4 q^{9/2}-9 q^{7/2}+14 q^{5/2}-20 q^{3/2}+22 \sqrt{q}-\frac{23}{\sqrt{q}}+\frac{20}{q^{3/2}}-\frac{15}{q^{5/2}}+\frac{9}{q^{7/2}}-\frac{4}{q^{9/2}}+\frac{1}{q^{11/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a z 7 + z 7 a -1 - a 3 z 5 + 3 a z 5 + 3 z 5 a -1 - z 5 a -3 -2 a 3 z 3 + 3 a z 3 + 3 z 3 a -1 -2 z 3 a -3 - a 3 z + a z + 2 z a -1 - z a -3 + a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$-3 z 10 a -2 -3 z 10 -10 a z 9 -16 z 9 a -1 -6 z 9 a -3 -15 a 2 z 8 -5 z 8 a -2 -4 z 8 a -4 -16 z 8 -14 a 3 z 7 + 8 a z 7 + 40 z 7 a -1 + 17 z 7 a -3 - z 7 a -5 -9 a 4 z 6 + 24 a 2 z 6 + 37 z 6 a -2 + 13 z 6 a -4 + 57 z 6 -4 a 5 z 5 + 19 a 3 z 5 + 17 a z 5 -20 z 5 a -1 -11 z 5 a -3 + 3 z 5 a -5 - a 6 z 4 + 7 a 4 z 4 -11 a 2 z 4 -38 z 4 a -2 -13 z 4 a -4 -44 z 4 + a 5 z 3 -10 a 3 z 3 -15 a z 3 -2 z 3 a -1 - z 3 a -3 -3 z 3 a -5 -2 a 4 z 2 + 2 a 2 z 2 + 10 z 2 a -2 + 4 z 2 a -4 + 10 z 2 + 2 a 3 z + 3 a z + z a -5 - a -2 + a -1 z -1 + a -3 z -1$ (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 =

-1 is the signature of L11a210. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -5$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -2$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = -1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 0$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{12}$
$r = 1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 2$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{12}$
$r = 3$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 5$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 6$	${\mathbb Z}_2$	${\mathbb Z}$