L11a140

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 2 u 4 + 2 v u 4 - u 4 + 5 v 2 u 3 -10 v u 3 + 5 u 3 -8 v 2 u 2 + 17 v u 2 -8 u 2 + 5 v 2 u -10 v u + 5 u - v 2 + 2 v -1$ (db)
Jones polynomial	$-q^{7/2}+5 q^{5/2}-11 q^{3/2}+17 \sqrt{q}-\frac{24}{\sqrt{q}}+\frac{26}{q^{3/2}}-\frac{26}{q^{5/2}}+\frac{22}{q^{7/2}}-\frac{16}{q^{9/2}}+\frac{9}{q^{11/2}}-\frac{4}{q^{13/2}}+\frac{1}{q^{15/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$- z a 7 + 3 z 3 a 5 + 3 z a 5 -3 z 5 a 3 -6 z 3 a 3 -3 z a 3 + a 3 z -1 + z 7 a + 3 z 5 a + 4 z 3 a - a z -1 - z 5 a -1 - z 3 a -1$ (db)
Kauffman polynomial	$-2 a 4 z 10 -2 a 2 z 10 -6 a 5 z 9 -14 a 3 z 9 -8 a z 9 -7 a 6 z 8 -18 a 4 z 8 -24 a 2 z 8 -13 z 8 -4 a 7 z 7 + a 5 z 7 + 9 a 3 z 7 -7 a z 7 -11 z 7 a -1 - a 8 z 6 + 14 a 6 z 6 + 47 a 4 z 6 + 53 a 2 z 6 -5 z 6 a -2 + 16 z 6 + 9 a 7 z 5 + 20 a 5 z 5 + 29 a 3 z 5 + 34 a z 5 + 15 z 5 a -1 - z 5 a -3 + 2 a 8 z 4 -9 a 6 z 4 -34 a 4 z 4 -31 a 2 z 4 + 4 z 4 a -2 -4 z 4 -7 a 7 z 3 -21 a 5 z 3 -29 a 3 z 3 -21 a z 3 -6 z 3 a -1 - a 8 z 2 + 2 a 6 z 2 + 8 a 4 z 2 + 6 a 2 z 2 + z 2 + 2 a 7 z + 6 a 5 z + 5 a 3 z + a z - a 2 + a 3 z -1 + a z -1$ (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 L11a140. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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