L11a465

(Knotscape image)

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

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

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$2 v u 3 -2 v w u 3 + 2 w u 3 -2 u 3 -5 v u 2 + 5 v w u 2 -5 w u 2 + 5 u 2 + 5 v u -5 v w u + 5 w u -5 u -2 v + 2 v w -2 w + 2$ (db)
Jones polynomial	$- q 8 + 4 q 7 -9 q 6 + 13 q 5 -16 q 4 + 19 q 3 -17 q 2 + 15 q -9 + 6 q -1 -2 q -2 + q -3$ (db)
Signature	2 (db)
HOMFLY-PT polynomial	$z 6 a -2 + z 6 a -4 + 2 z 4 a -2 + 2 z 4 a -4 - z 4 a -6 -2 z 4 + a 2 z 2 + 3 z 2 a -2 + 2 z 2 a -4 - z 2 a -6 -5 z 2 + 2 a 2 + 3 a -2 + a -4 - a -6 -5 + a 2 z -2 + a -2 z -2 -2 z -2$ (db)
Kauffman polynomial	$z 10 a -2 + z 10 a -4 + 2 z 9 a -1 + 7 z 9 a -3 + 5 z 9 a -5 + 5 z 8 a -2 + 12 z 8 a -4 + 9 z 8 a -6 + 2 z 8 + 2 a z 7 + z 7 a -1 -11 z 7 a -3 -2 z 7 a -5 + 8 z 7 a -7 + a 2 z 6 -9 z 6 a -2 -31 z 6 a -4 -18 z 6 a -6 + 4 z 6 a -8 + z 6 -5 a z 5 -5 z 5 a -1 + 8 z 5 a -3 -7 z 5 a -5 -14 z 5 a -7 + z 5 a -9 -4 a 2 z 4 + 31 z 4 a -4 + 15 z 4 a -6 -5 z 4 a -8 -15 z 4 + 2 a z 3 -4 z 3 a -1 -5 z 3 a -3 + 8 z 3 a -5 + 6 z 3 a -7 - z 3 a -9 + 6 a 2 z 2 + 7 z 2 a -2 -13 z 2 a -4 -7 z 2 a -6 + 19 z 2 + 3 a z + 7 z a -1 + 3 z a -3 -3 z a -5 -2 z a -7 -4 a 2 -6 a -2 + 2 a -4 + 2 a -6 -9-2 a z -1 -2 a -1 z -1 + a 2 z -2 + a -2 z -2 + 2 z -2$ (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 =

2 is the signature of L11a465. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

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