L11a475

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$3 v u 3 - v w u 3 + w u 3 -3 u 3 -7 v u 2 + 5 v w u 2 -5 w u 2 + 7 u 2 + 5 v u -7 v w u + 7 w u -5 u - v + 3 v w -3 w + 1$ (db)
Jones polynomial	$- q 5 + 4 q 4 -9 q 3 + 15 q 2 -19 q + 21-20 q -1 + 18 q -2 -11 q -3 + 7 q -4 -2 q -5 + q -6$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$a 6 z -2 + a 6 -3 z 2 a 4 -2 a 4 z -2 -4 a 4 + 3 z 4 a 2 + 4 z 2 a 2 + a 2 z -2 + 3 a 2 - z 6 - z 4 - z 2 + 2 z 4 a -2 + z 2 a -2 - z 2 a -4$ (db)
Kauffman polynomial	$a 2 z 10 + z 10 + 3 a 3 z 9 + 8 a z 9 + 5 z 9 a -1 + 3 a 4 z 8 + 11 a 2 z 8 + 9 z 8 a -2 + 17 z 8 + 2 a 5 z 7 -3 a z 7 + 7 z 7 a -1 + 8 z 7 a -3 + a 6 z 6 -3 a 4 z 6 -27 a 2 z 6 -11 z 6 a -2 + 4 z 6 a -4 -38 z 6 -4 a 5 z 5 -7 a 3 z 5 -18 a z 5 -28 z 5 a -1 -12 z 5 a -3 + z 5 a -5 -4 a 6 z 4 -5 a 4 z 4 + 22 a 2 z 4 + 3 z 4 a -2 -5 z 4 a -4 + 31 z 4 + 4 a 3 z 3 + 18 a z 3 + 22 z 3 a -1 + 7 z 3 a -3 - z 3 a -5 + 6 a 6 z 2 + 9 a 4 z 2 -7 a 2 z 2 -2 z 2 a -2 + 2 z 2 a -4 -14 z 2 + 4 a 5 z + 2 a 3 z -6 a z -6 z a -1 -2 z a -3 -4 a 6 -6 a 4 - a 2 + a -2 + 3-2 a 5 z -1 -2 a 3 z -1 + a 6 z -2 + 2 a 4 z -2 + a 2 z -2$ (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 L11a475. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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