L11n92

(Knotscape image)

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

Visit L11n92's page at the original Knot Atlas.

Planar diagram presentation	X₆₁₇₂ X_12,4,13,3 X_7,16,8,17 X_20,12,21,11 X_22,18,5,17 X_18,22,19,21 X_10,20,11,19 X_9,14,10,15 X_15,8,16,9 X₂₅₃₆ X_4,14,1,13
Gauss code	{1, -10, 2, -11}, {10, -1, -3, 9, -8, -7, 4, -2, 11, 8, -9, 3, 5, -6, 7, -4, 6, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-2 v u 3 + 2 u 3 + 6 v u 2 -6 u 2 -6 v u + 6 u + 2 v -2$ (db)
Jones polynomial	$-q^{13/2}+4 q^{11/2}-7 q^{9/2}+9 q^{7/2}-11 q^{5/2}+11 q^{3/2}-10 \sqrt{q}+\frac{6}{\sqrt{q}}-\frac{4}{q^{3/2}}+\frac{1}{q^{5/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$z 5 a -1 + z 5 a -3 - a z 3 + z 3 a -1 + z 3 a -3 - z 3 a -5 + a z -1 - a -1 z -1$ (db)
Kauffman polynomial	$- z 9 a -1 - z 9 a -3 -5 z 8 a -2 -4 z 8 a -4 - z 8 -6 z 7 a -3 -6 z 7 a -5 + 8 z 6 a -2 + 4 z 6 a -4 -4 z 6 a -6 -4 a z 5 -4 z 5 a -1 + 13 z 5 a -3 + 12 z 5 a -5 - z 5 a -7 - a 2 z 4 -6 z 4 a -2 + 3 z 4 a -4 + 7 z 4 a -6 -3 z 4 + 5 a z 3 + 4 z 3 a -1 -6 z 3 a -3 -4 z 3 a -5 + z 3 a -7 + a 2 z 2 -2 z 2 a -4 - z 2 a -6 + 2 z 2 + 1- a z -1 - a -1 z -1$ (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 L11n92. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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