L11a6

(Knotscape image)

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

Visit L11a6's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_14,7,15,8 X_4,15,1,16 X_12,6,13,5 X₈₄₉₃ X_16,10,17,9 X_20,12,21,11 X_22,18,5,17 X_18,22,19,21 X_10,20,11,19 X_2,14,3,13
Gauss code	{1, -11, 5, -3}, {4, -1, 2, -5, 6, -10, 7, -4, 11, -2, 3, -6, 8, -9, 10, -7, 9, -8}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$\frac{(u-1) (v-1) \left(2 v^4-4 v^3+5 v^2-4 v+2\right)}{\sqrt{u} v^{5/2}}$ (db)
Jones polynomial	$22 q^{9/2}-22 q^{7/2}+18 q^{5/2}-15 q^{3/2}+\frac{1}{q^{3/2}}-q^{19/2}+4 q^{17/2}-8 q^{15/2}+14 q^{13/2}-19 q^{11/2}+8 \sqrt{q}-\frac{4}{\sqrt{q}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$- z 5 a -7 -2 z 3 a -7 + a -7 z -1 + z 7 a -5 + 3 z 5 a -5 + 2 z 3 a -5 -2 z a -5 -2 a -5 z -1 + z 7 a -3 + 3 z 5 a -3 + 3 z 3 a -3 + 2 z a -3 - z 5 a -1 -2 z 3 a -1 + a -1 z -1$ (db)
Kauffman polynomial	$z 5 a -11 - z 3 a -11 + 4 z 6 a -10 -6 z 4 a -10 + 2 z 2 a -10 + 7 z 7 a -9 -10 z 5 a -9 + 4 z 3 a -9 + 8 z 8 a -8 -9 z 6 a -8 + 5 z 2 a -8 -2 a -8 + 6 z 9 a -7 -2 z 7 a -7 -6 z 5 a -7 + 4 z 3 a -7 + a -7 z -1 + 2 z 10 a -6 + 11 z 8 a -6 -22 z 6 a -6 + 6 z 4 a -6 + 9 z 2 a -6 -5 a -6 + 11 z 9 a -5 -15 z 7 a -5 + z 5 a -5 + 3 z 3 a -5 -3 z a -5 + 2 a -5 z -1 + 2 z 10 a -4 + 9 z 8 a -4 -21 z 6 a -4 + 4 z 4 a -4 + 7 z 2 a -4 -3 a -4 + 5 z 9 a -3 -2 z 7 a -3 -14 z 5 a -3 + 12 z 3 a -3 -4 z a -3 + 6 z 8 a -2 -11 z 6 a -2 + 2 z 4 a -2 + 2 z 2 a -2 + a -2 + 4 z 7 a -1 -10 z 5 a -1 + 8 z 3 a -1 - z a -1 - a -1 z -1 + z 6 -2 z 4 + z 2$ (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 L11a6. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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