L11a485

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$\frac{(u-1) (v-1) (w-1)^3 \left(w^2-w+1\right)}{\sqrt{u} \sqrt{v} w^{5/2}}$ (db)
Jones polynomial	$- q 5 + 5 q 4 -11 q 3 + 19 q 2 -26 q + 32-30 q -1 + 28 q -2 -20 q -3 + 13 q -4 -6 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$z 8 -2 a 2 z 6 - z 6 a -2 + 4 z 6 + a 4 z 4 -4 a 2 z 4 -2 z 4 a -2 + 5 z 4 + 2 a 2 z 2 -2 z 2 -2 a 4 + 6 a 2 + 2 a -2 -6 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$4 a 2 z 10 + 4 z 10 + 12 a 3 z 9 + 24 a z 9 + 12 z 9 a -1 + 13 a 4 z 8 + 24 a 2 z 8 + 15 z 8 a -2 + 26 z 8 + 6 a 5 z 7 -14 a 3 z 7 -36 a z 7 -5 z 7 a -1 + 11 z 7 a -3 + a 6 z 6 -26 a 4 z 6 -69 a 2 z 6 -20 z 6 a -2 + 5 z 6 a -4 -67 z 6 -8 a 5 z 5 -8 a 3 z 5 -3 a z 5 -17 z 5 a -1 -13 z 5 a -3 + z 5 a -5 + 12 a 4 z 4 + 38 a 2 z 4 + 8 z 4 a -2 -4 z 4 a -4 + 38 z 4 + 2 a 3 z 3 + 10 a z 3 + 12 z 3 a -1 + 4 z 3 a -3 + 2 a 4 z 2 + 10 a 2 z 2 + 2 z 2 a -2 + 10 z 2 + 2 a 5 z + 6 a 3 z + 6 a z + 2 z a -1 -4 a 4 -12 a 2 -4 a -2 -11-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 =

0 is the signature of L11a485. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = -1$	$i = 1$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -3$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{8}$	${\mathbb Z}^{8}$
$r = -2$	${\mathbb Z}^{16}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = -1$	${\mathbb Z}^{14}\oplus{\mathbb Z}_2^{16}$	${\mathbb Z}^{16}$
$r = 0$	${\mathbb Z}^{18}\oplus{\mathbb Z}_2^{14}$	${\mathbb Z}^{18}$
$r = 1$	${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{14}$	${\mathbb Z}^{14}$
$r = 2$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{12}$	${\mathbb Z}^{12}$
$r = 3$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$