L11a29

(Knotscape image)

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

Visit L11a29's page at the original Knot Atlas.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-5 v u 3 + 5 u 3 + 13 v u 2 -13 u 2 -13 v u + 13 u + 5 v -5$ (db)
Jones polynomial	$q^{21/2}-4 q^{19/2}+10 q^{17/2}-15 q^{15/2}+21 q^{13/2}-24 q^{11/2}+22 q^{9/2}-21 q^{7/2}+14 q^{5/2}-8 q^{3/2}+3 \sqrt{q}-\frac{1}{\sqrt{q}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$- z 5 a -3 -3 z 5 a -5 - z 5 a -7 + z 3 a -1 + z 3 a -3 -6 z 3 a -5 + z 3 a -7 + z 3 a -9 + z a -1 + 3 z a -3 -5 z a -5 + z a -7 + 2 a -3 z -1 -2 a -5 z -1 - a -7 z -1 + a -9 z -1$ (db)
Kauffman polynomial	$-2 z 10 a -6 -2 z 10 a -8 -6 z 9 a -5 -13 z 9 a -7 -7 z 9 a -9 -8 z 8 a -4 -16 z 8 a -6 -16 z 8 a -8 -8 z 8 a -10 -6 z 7 a -3 -2 z 7 a -5 + 17 z 7 a -7 + 9 z 7 a -9 -4 z 7 a -11 -3 z 6 a -2 + 11 z 6 a -4 + 42 z 6 a -6 + 48 z 6 a -8 + 19 z 6 a -10 - z 6 a -12 - z 5 a -1 + 9 z 5 a -3 + 23 z 5 a -5 + 8 z 5 a -7 + 3 z 5 a -9 + 8 z 5 a -11 + 4 z 4 a -2 -7 z 4 a -4 -37 z 4 a -6 -44 z 4 a -8 -16 z 4 a -10 + 2 z 4 a -12 + 2 z 3 a -1 -9 z 3 a -3 -31 z 3 a -5 -19 z 3 a -7 -3 z 3 a -9 -4 z 3 a -11 - z 2 a -2 -2 z 2 a -4 + 14 z 2 a -6 + 25 z 2 a -8 + 9 z 2 a -10 - z 2 a -12 - z a -1 + 7 z a -3 + 15 z a -5 + 9 z a -7 + 2 z a -9 + 2 a -4 -4 a -6 -9 a -8 -4 a -10 -2 a -3 z -1 -2 a -5 z -1 + a -7 z -1 + a -9 z -1$ (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 =

3 is the signature of L11a29. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 2$	$i = 4$
$r = -2$	${\mathbb Z}$
$r = -1$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = 0$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{4}$
$r = 1$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 3$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 4$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 5$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = 6$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = 7$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 8$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 9$	${\mathbb Z}_2$	${\mathbb Z}$