L10a28

(Knotscape image)

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

Visit L10a28's page at the original Knot Atlas.

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v u 5 + u 5 + 3 v u 4 -3 u 4 -5 v u 3 + 5 u 3 + 5 v u 2 -5 u 2 -3 v u + 3 u + v -1$ (db)
Jones polynomial	$-q^{7/2}+3 q^{5/2}-6 q^{3/2}+8 \sqrt{q}-\frac{12}{\sqrt{q}}+\frac{12}{q^{3/2}}-\frac{11}{q^{5/2}}+\frac{9}{q^{7/2}}-\frac{6}{q^{9/2}}+\frac{3}{q^{11/2}}-\frac{1}{q^{13/2}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a z 7 -2 a 3 z 5 + 5 a z 5 - z 5 a -1 + a 5 z 3 -7 a 3 z 3 + 10 a z 3 -3 z 3 a -1 + 2 a 5 z -8 a 3 z + 9 a z -3 z a -1 + a 5 z -1 -3 a 3 z -1 + 4 a z -1 -2 a -1 z -1$ (db)
Kauffman polynomial	$- a 3 z 9 - a z 9 -3 a 4 z 8 -7 a 2 z 8 -4 z 8 -4 a 5 z 7 -8 a 3 z 7 -9 a z 7 -5 z 7 a -1 -3 a 6 z 6 + 13 a 2 z 6 -3 z 6 a -2 + 7 z 6 - a 7 z 5 + 6 a 5 z 5 + 24 a 3 z 5 + 31 a z 5 + 13 z 5 a -1 - z 5 a -3 + 6 a 6 z 4 + 9 a 4 z 4 -7 a 2 z 4 + 6 z 4 a -2 -4 z 4 + 2 a 7 z 3 - a 5 z 3 -28 a 3 z 3 -40 a z 3 -13 z 3 a -1 + 2 z 3 a -3 -3 a 6 z 2 -8 a 4 z 2 -5 a 2 z 2 - z 2 a -2 - z 2 - a 7 z + 2 a 5 z + 15 a 3 z + 19 a z + 7 z a -1 + a 6 + 3 a 4 + 3 a 2 + 2- a 5 z -1 -3 a 3 z -1 -4 a z -1 -2 a -1 z -1$ (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 L10a28. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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