L11a70

(Knotscape image)

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

Visit L11a70's page at the original Knot Atlas.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 5 + 2 u 5 + 5 v u 4 -7 u 4 -10 v u 3 + 10 u 3 + 10 v u 2 -10 u 2 -7 v u + 5 u + 2 v -1$ (db)
Jones polynomial	$q^{3/2}-5 \sqrt{q}+\frac{10}{\sqrt{q}}-\frac{16}{q^{3/2}}+\frac{20}{q^{5/2}}-\frac{23}{q^{7/2}}+\frac{22}{q^{9/2}}-\frac{19}{q^{11/2}}+\frac{13}{q^{13/2}}-\frac{7}{q^{15/2}}+\frac{3}{q^{17/2}}-\frac{1}{q^{19/2}}$ (db)
Signature	-3 (db)
HOMFLY-PT polynomial	$z a 9 + a 9 z -1 -3 z 3 a 7 -6 z a 7 -3 a 7 z -1 + 3 z 5 a 5 + 8 z 3 a 5 + 8 z a 5 + 4 a 5 z -1 - z 7 a 3 -3 z 5 a 3 -4 z 3 a 3 -4 z a 3 -2 a 3 z -1 + z 5 a + z 3 a - z a$ (db)
Kauffman polynomial	$- z 5 a 11 + 2 z 3 a 11 - z a 11 -3 z 6 a 10 + 5 z 4 a 10 -3 z 2 a 10 + a 10 -5 z 7 a 9 + 6 z 5 a 9 -3 z 3 a 9 + 2 z a 9 - a 9 z -1 -6 z 8 a 8 + 4 z 6 a 8 + 4 z 4 a 8 -8 z 2 a 8 + 3 a 8 -5 z 9 a 7 -2 z 7 a 7 + 17 z 5 a 7 -24 z 3 a 7 + 13 z a 7 -3 a 7 z -1 -2 z 10 a 6 -12 z 8 a 6 + 28 z 6 a 6 -16 z 4 a 6 -4 z 2 a 6 + 3 a 6 -12 z 9 a 5 + 14 z 7 a 5 + 15 z 5 a 5 -30 z 3 a 5 + 18 z a 5 -4 a 5 z -1 -2 z 10 a 4 -15 z 8 a 4 + 42 z 6 a 4 -26 z 4 a 4 + 2 z 2 a 4 + 2 a 4 -7 z 9 a 3 + 6 z 7 a 3 + 15 z 5 a 3 -15 z 3 a 3 + 7 z a 3 -2 a 3 z -1 -9 z 8 a 2 + 20 z 6 a 2 -10 z 4 a 2 + z 2 a 2 -5 z 7 a + 10 z 5 a -4 z 3 a - z a - z 6 + z 4$ (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 =

-3 is the signature of L11a70. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -4$	$i = -2$
$r = -8$	${\mathbb Z}$
$r = -7$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -6$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{2}$
$r = -5$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -4$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{9}$
$r = -3$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = -2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = -1$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 0$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{10}$
$r = 1$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 2$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 3$	${\mathbb Z}_2$	${\mathbb Z}$