L11a107

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_14,3,15,4 X_22,15,5,16 X_16,7,17,8 X_18,9,19,10 X_20,11,21,12 X_8,17,9,18 X_10,19,11,20 X_12,21,13,22 X₂₅₃₆ X_4,13,1,14
Gauss code	{1, -10, 2, -11}, {10, -1, 4, -7, 5, -8, 6, -9, 11, -2, 3, -4, 7, -5, 8, -6, 9, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- u 7 -2 v u 6 + 2 u 6 + 2 v u 5 -2 u 5 -2 v u 4 + 2 u 4 + 2 v u 3 -2 u 3 -2 v u 2 + 2 u 2 + 2 v u -2 u - v$ (db)
Jones polynomial	$-\frac{1}{q^{7/2}}+\frac{2}{q^{9/2}}-\frac{4}{q^{11/2}}+\frac{4}{q^{13/2}}-\frac{7}{q^{15/2}}+\frac{7}{q^{17/2}}-\frac{8}{q^{19/2}}+\frac{7}{q^{21/2}}-\frac{5}{q^{23/2}}+\frac{4}{q^{25/2}}-\frac{2}{q^{27/2}}+\frac{1}{q^{29/2}}$ (db)
Signature	-7 (db)
HOMFLY-PT polynomial	$- z 3 a 13 -4 z a 13 -3 a 13 z -1 + 3 z 5 a 11 + 15 z 3 a 11 + 20 z a 11 + 7 a 11 z -1 -2 z 7 a 9 -12 z 5 a 9 -23 z 3 a 9 -17 z a 9 -4 a 9 z -1 - z 7 a 7 -5 z 5 a 7 -6 z 3 a 7 - z a 7$ (db)
Kauffman polynomial	$- z 4 a 18 + 2 z 2 a 18 - a 18 -2 z 5 a 17 + 3 z 3 a 17 -2 z 6 a 16 + z 4 a 16 + 2 z 2 a 16 -2 z 7 a 15 + 2 z 5 a 15 - z 3 a 15 -2 z 8 a 14 + 4 z 6 a 14 -4 z 4 a 14 -2 z 9 a 13 + 7 z 7 a 13 -12 z 5 a 13 + 12 z 3 a 13 -10 z a 13 + 3 a 13 z -1 - z 10 a 12 + z 8 a 12 + 9 z 6 a 12 -24 z 4 a 12 + 22 z 2 a 12 -7 a 12 -5 z 9 a 11 + 27 z 7 a 11 -55 z 5 a 11 + 57 z 3 a 11 -29 z a 11 + 7 a 11 z -1 - z 10 a 10 + z 8 a 10 + 12 z 6 a 10 -27 z 4 a 10 + 23 z 2 a 10 -7 a 10 -3 z 9 a 9 + 17 z 7 a 9 -34 z 5 a 9 + 35 z 3 a 9 -18 z a 9 + 4 a 9 z -1 -2 z 8 a 8 + 9 z 6 a 8 -9 z 4 a 8 + z 2 a 8 - z 7 a 7 + 5 z 5 a 7 -6 z 3 a 7 + z a 7$ (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 =

-7 is the signature of L11a107. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -8$	$i = -6$
$r = -11$	${\mathbb Z}$
$r = -10$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -9$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -8$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -7$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -6$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -5$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -4$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{5}$
$r = -3$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -2$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -1$	${\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = 0$	${\mathbb Z}$	${\mathbb Z}$