L11a97

(Knotscape image)

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

Visit L11a97's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_16,7,17,8 X_20,17,21,18 X_18,13,19,14 X_14,19,15,20 X_4,21,1,22 X_10,5,11,6 X_12,3,13,4 X_22,11,5,12 X_2,9,3,10 X_8,15,9,16
Gauss code	{1, -10, 8, -6}, {7, -1, 2, -11, 10, -7, 9, -8, 4, -5, 11, -2, 3, -4, 5, -3, 6, -9}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- u 5 -6 v u 4 + 6 u 4 + 13 v u 3 -13 u 3 -13 v u 2 + 13 u 2 + 6 v u -6 u - v$ (db)
Jones polynomial	$-\frac{1}{q^{5/2}}+\frac{4}{q^{7/2}}-\frac{11}{q^{9/2}}+\frac{16}{q^{11/2}}-\frac{23}{q^{13/2}}+\frac{25}{q^{15/2}}-\frac{25}{q^{17/2}}+\frac{22}{q^{19/2}}-\frac{15}{q^{21/2}}+\frac{9}{q^{23/2}}-\frac{4}{q^{25/2}}+\frac{1}{q^{27/2}}$ (db)
Signature	-5 (db)
HOMFLY-PT polynomial	$- z a 13 + 3 z 3 a 11 + 2 z a 11 -2 a 11 z -1 -2 z 5 a 9 + 7 z a 9 + 5 a 9 z -1 -4 z 5 a 7 -11 z 3 a 7 -10 z a 7 -3 a 7 z -1 - z 5 a 5 - z 3 a 5$ (db)
Kauffman polynomial	$- z 6 a 16 + 2 z 4 a 16 - z 2 a 16 -4 z 7 a 15 + 9 z 5 a 15 -6 z 3 a 15 + z a 15 -7 z 8 a 14 + 15 z 6 a 14 -11 z 4 a 14 + 4 z 2 a 14 - a 14 -6 z 9 a 13 + 3 z 7 a 13 + 14 z 5 a 13 -13 z 3 a 13 + 2 z a 13 -2 z 10 a 12 -17 z 8 a 12 + 48 z 6 a 12 -41 z 4 a 12 + 14 z 2 a 12 -14 z 9 a 11 + 15 z 7 a 11 + 12 z 5 a 11 -14 z 3 a 11 + 4 z a 11 -2 a 11 z -1 -2 z 10 a 10 -22 z 8 a 10 + 52 z 6 a 10 -34 z 4 a 10 + 2 z 2 a 10 + 5 a 10 -8 z 9 a 9 -2 z 7 a 9 + 25 z 5 a 9 -24 z 3 a 9 + 13 z a 9 -5 a 9 z -1 -12 z 8 a 8 + 16 z 6 a 8 -3 z 4 a 8 -7 z 2 a 8 + 5 a 8 -10 z 7 a 7 + 17 z 5 a 7 -16 z 3 a 7 + 10 z a 7 -3 a 7 z -1 -4 z 6 a 6 + 3 z 4 a 6 - z 5 a 5 + z 3 a 5$ (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 L11a97. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -6$	$i = -4$
$r = -11$	${\mathbb Z}$
$r = -10$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -9$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -8$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = -7$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -6$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{13}$
$r = -5$	${\mathbb Z}^{13}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = -4$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{13}$	${\mathbb Z}^{14}$
$r = -3$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = -2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = -1$	${\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 0$	${\mathbb Z}$	${\mathbb Z}$