L11a207

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v 2 u 4 + 3 v u 4 - u 4 + 6 v 2 u 3 -10 v u 3 + 4 u 3 -7 v 2 u 2 + 15 v u 2 -7 u 2 + 4 v 2 u -10 v u + 6 u - v 2 + 3 v -2$ (db)
Jones polynomial	$q^{15/2}-5 q^{13/2}+11 q^{11/2}-17 q^{9/2}+23 q^{7/2}-27 q^{5/2}+25 q^{3/2}-23 \sqrt{q}+\frac{16}{\sqrt{q}}-\frac{9}{q^{3/2}}+\frac{4}{q^{5/2}}-\frac{1}{q^{7/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 7 a -1 - z 7 a -3 + a z 5 -3 z 5 a -1 -2 z 5 a -3 + z 5 a -5 + 2 a z 3 -4 z 3 a -1 + z 3 a -3 + z 3 a -5 + a z -2 z a -1 + 3 z a -3 - z a -5 + a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$-3 z 10 a -2 -3 z 10 a -4 -8 z 9 a -1 -17 z 9 a -3 -9 z 9 a -5 -16 z 8 a -2 -16 z 8 a -4 -10 z 8 a -6 -10 z 8 -8 a z 7 + z 7 a -1 + 26 z 7 a -3 + 12 z 7 a -5 -5 z 7 a -7 -4 a 2 z 6 + 39 z 6 a -2 + 47 z 6 a -4 + 22 z 6 a -6 - z 6 a -8 + 11 z 6 - a 3 z 5 + 11 a z 5 + 16 z 5 a -1 + 5 z 5 a -5 + 9 z 5 a -7 + 5 a 2 z 4 -23 z 4 a -2 -29 z 4 a -4 -12 z 4 a -6 + z 4 a -8 -2 z 4 + a 3 z 3 -7 a z 3 -16 z 3 a -1 -12 z 3 a -3 -7 z 3 a -5 -3 z 3 a -7 -2 a 2 z 2 + 2 z 2 a -2 + 2 z 2 a -4 -2 z 2 + 2 a z + 5 z a -1 + 5 z a -3 + 2 z a -5 - a -2 + a -1 z -1 + a -3 z -1$ (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 L11a207. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 0$	$i = 2$
$r = -4$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -2$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -1$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 0$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{11}$
$r = 1$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = 2$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{14}$
$r = 3$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = 4$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 5$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 6$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 7$	${\mathbb Z}_2$	${\mathbb Z}$