L11a2

(Knotscape image)

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

Visit L11a2's page at the original Knot Atlas.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 5 + u 5 + 6 v u 4 -6 u 4 -14 v u 3 + 14 u 3 + 14 v u 2 -14 u 2 -6 v u + 6 u + v -1$ (db)
Jones polynomial	$q^{9/2}-5 q^{7/2}+10 q^{5/2}-17 q^{3/2}+23 \sqrt{q}-\frac{27}{\sqrt{q}}+\frac{27}{q^{3/2}}-\frac{24}{q^{5/2}}+\frac{17}{q^{7/2}}-\frac{11}{q^{9/2}}+\frac{5}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a z 7 -2 a 3 z 5 + 3 a z 5 -2 z 5 a -1 + a 5 z 3 -3 a 3 z 3 + 5 a z 3 -3 z 3 a -1 + z 3 a -3 - a 3 z + a z + a 3 z -1 -2 a z -1 + 2 a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$-2 a 2 z 10 -2 z 10 -8 a 3 z 9 -15 a z 9 -7 z 9 a -1 -13 a 4 z 8 -26 a 2 z 8 -9 z 8 a -2 -22 z 8 -11 a 5 z 7 -8 a 3 z 7 + 9 a z 7 + z 7 a -1 -5 z 7 a -3 -5 a 6 z 6 + 16 a 4 z 6 + 58 a 2 z 6 + 19 z 6 a -2 - z 6 a -4 + 57 z 6 - a 7 z 5 + 15 a 5 z 5 + 35 a 3 z 5 + 32 a z 5 + 23 z 5 a -1 + 10 z 5 a -3 + 4 a 6 z 4 -5 a 4 z 4 -35 a 2 z 4 -12 z 4 a -2 + z 4 a -4 -39 z 4 -6 a 5 z 3 -21 a 3 z 3 -27 a z 3 -17 z 3 a -1 -5 z 3 a -3 + a 4 z 2 + 6 a 2 z 2 + 2 z 2 a -2 + 7 z 2 + a 3 z -2 z a -1 - z a -3 + 1 + a 3 z -1 + 2 a z -1 + 2 a -1 z -1 + a -3 z -1$ (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 L11a2. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -2$	$i = 0$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = -3$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = -2$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = -1$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{14}$	${\mathbb Z}^{14}$
$r = 0$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{15}$
$r = 1$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = 2$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 3$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$