L11n103

(Knotscape image)

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

Planar diagram presentation	X₆₁₇₂ X_12,3,13,4 X_7,16,8,17 X_17,22,18,5 X_13,18,14,19 X_21,14,22,15 X_9,20,10,21 X_15,8,16,9 X_19,10,20,11 X₂₅₃₆ X_4,11,1,12
Gauss code	{1, -10, 2, -11}, {10, -1, -3, 8, -7, 9, 11, -2, -5, 6, -8, 3, -4, 5, -9, 7, -6, 4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-3 v u 3 - u 3 + 3 v u 2 + 3 u - v -3$ (db)
Jones polynomial	$-\frac{1}{q^{5/2}}+\frac{2}{q^{7/2}}-\frac{4}{q^{9/2}}+\frac{4}{q^{11/2}}-\frac{5}{q^{13/2}}+\frac{3}{q^{15/2}}-\frac{3}{q^{17/2}}+\frac{1}{q^{19/2}}+\frac{1}{q^{21/2}}-\frac{1}{q^{23/2}}+\frac{1}{q^{25/2}}$ (db)
Signature	-5 (db)
HOMFLY-PT polynomial	$- a 13 z -1 + 2 z a 11 + a 11 z -1 + z 3 a 9 + 4 z a 9 + 2 a 9 z -1 -2 z 5 a 7 -8 z 3 a 7 -7 z a 7 -2 a 7 z -1 - z 5 a 5 -3 z 3 a 5 - z a 5$ (db)
Kauffman polynomial	$- z 8 a 14 + 7 z 6 a 14 -15 z 4 a 14 + 13 z 2 a 14 -4 a 14 - z 9 a 13 + 7 z 7 a 13 -13 z 5 a 13 + 7 z 3 a 13 - z a 13 + a 13 z -1 -2 z 8 a 12 + 17 z 6 a 12 -41 z 4 a 12 + 34 z 2 a 12 -9 a 12 - z 9 a 11 + 7 z 7 a 11 -12 z 5 a 11 + 2 z 3 a 11 + z a 11 + a 11 z -1 -2 z 8 a 10 + 13 z 6 a 10 -27 z 4 a 10 + 17 z 2 a 10 -4 a 10 -3 z 7 a 9 + 13 z 5 a 9 -21 z 3 a 9 + 12 z a 9 -2 a 9 z -1 - z 8 a 8 + z 6 a 8 + 4 z 4 a 8 -5 z 2 a 8 + 2 a 8 -3 z 7 a 7 + 11 z 5 a 7 -13 z 3 a 7 + 9 z a 7 -2 a 7 z -1 -2 z 6 a 6 + 5 z 4 a 6 - z 2 a 6 - z 5 a 5 + 3 z 3 a 5 - z a 5$ (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 =

-5 is the signature of L11n103. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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