L11a187

(Knotscape image)

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

Planar diagram presentation	X₈₁₉₂ X_10,3,11,4 X_20,14,21,13 X_16,5,17,6 X_4,15,5,16 X_18,12,19,11 X_22,18,7,17 X_14,20,15,19 X_12,22,13,21 X₂₇₃₈ X_6,9,1,10
Gauss code	{1, -10, 2, -5, 4, -11}, {10, -1, 11, -2, 6, -9, 3, -8, 5, -4, 7, -6, 8, -3, 9, -7}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 4 -2 v 2 u 3 + 7 v u 3 -4 u 3 + 5 v 2 u 2 -11 v u 2 + 5 u 2 -4 v 2 u + 7 v u -2 u -2 v$ (db)
Jones polynomial	$q^{9/2}-3 q^{7/2}+6 q^{5/2}-10 q^{3/2}+14 \sqrt{q}-\frac{16}{\sqrt{q}}+\frac{16}{q^{3/2}}-\frac{15}{q^{5/2}}+\frac{10}{q^{7/2}}-\frac{7}{q^{9/2}}+\frac{3}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$z 3 a 5 + z a 5 + a 5 z -1 - z 5 a 3 - z 3 a 3 - z a 3 -2 z 5 a -4 z 3 a -4 z a -2 a z -1 - z 5 a -1 - z 3 a -1 + a -1 z -1 + z 3 a -3 + z a -3$ (db)
Kauffman polynomial	$- a 2 z 10 - z 10 -4 a 3 z 9 -7 a z 9 -3 z 9 a -1 -6 a 4 z 8 -9 a 2 z 8 -4 z 8 a -2 -7 z 8 -6 a 5 z 7 + 4 a 3 z 7 + 16 a z 7 + 3 z 7 a -1 -3 z 7 a -3 -3 a 6 z 6 + 12 a 4 z 6 + 29 a 2 z 6 + 10 z 6 a -2 - z 6 a -4 + 25 z 6 - a 7 z 5 + 15 a 5 z 5 + a 3 z 5 -20 a z 5 + 4 z 5 a -1 + 9 z 5 a -3 + 5 a 6 z 4 -9 a 4 z 4 -38 a 2 z 4 -7 z 4 a -2 + 3 z 4 a -4 -34 z 4 + 2 a 7 z 3 -15 a 5 z 3 -5 a 3 z 3 + 17 a z 3 -2 z 3 a -1 -7 z 3 a -3 + 19 a 2 z 2 + 4 z 2 a -2 -2 z 2 a -4 + 25 z 2 + 7 a 5 z -9 a z - z a -1 + z a -3 + a 4 -3 a 2 -2 a -2 -5- a 5 z -1 + 2 a z -1 + a -1 z -1$ (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 L11a187. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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