L7n1

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	[edit L7n1 Quick Notes] L7n1 is $7_{7}^{2}$ in the Rolfsen table of links.

Planar diagram presentation	X₆₁₇₂ X_12,7,13,8 X_4,13,1,14 X_5,10,6,11 X₃₈₄₉ X_9,14,10,5 X_11,2,12,3
Gauss code	{1, 7, -5, -3}, {-4, -1, 2, 5, -6, 4, -7, -2, 3, 6}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	${\frac {-uv^{3}-1}{{\sqrt {u}}v^{3/2}}}$ (db)
Jones polynomial	$-{\frac {1}{q^{5/2}}}-{\frac {1}{q^{9/2}}}-{\frac {1}{q^{13/2}}}+{\frac {1}{q^{15/2}}}$ (db)
Signature	-5 (db)
HOMFLY-PT polynomial	$-a^{9}z^{-1}+a^{7}z^{3}+4a^{7}z+3a^{7}z^{-1}-a^{5}z^{5}-5a^{5}z^{3}-6a^{5}z-2a^{5}z^{-1}$ (db)
Kauffman polynomial	$a^{10}+a^{9}z-a^{9}z^{-1}+a^{8}z^{4}-4a^{8}z^{2}+3a^{8}+a^{7}z^{5}-5a^{7}z^{3}+7a^{7}z-3a^{7}z^{-1}+a^{6}z^{4}-4a^{6}z^{2}+3a^{6}+a^{5}z^{5}-5a^{5}z^{3}+6a^{5}z-2a^{5}z^{-1}$ (db)

The coefficients of the monomials

t^{r}q^{j}

are shown, along with their alternating sums

\chi

(fixed

j

, alternation over

r

).

-5

-4

-3

-2

-1

0

χ

-4

1

-6

1

-8

1

-10

1

-12

2

1

-14

0

-16

1

-1

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