L2a1

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	[edit L2a1 Quick Notes] L2a1 is $2_{1}^{2}$ in Rolfsen's table of links. It is also known as the "Hopf Link".

Japanese family emblem	Linked hearts	expanded Kolam Two-hearts [1]	Logo
In Star of David form on old Jewish building in Prague	Three wreaths linked as two L2a1 configurations on Michelangelo's tomb	One form of a heterosexuality symbol	(pseudo-3D)
Are they forever linked? [2]	As impossible object	Linked hearts (pseudo-3D)	German coat of arms

Planar diagram presentation	X₄₁₃₂ X₂₃₁₄
Gauss code	{1, -2}, {2, -1}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-1$ (db)
Jones polynomial	$-{\frac {1}{\sqrt {q}}}-{\frac {1}{q^{5/2}}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a^{3}z^{-1}-za-az^{-1}$ (db)
Kauffman polynomial	$-za^{3}+a^{3}z^{-1}-a^{2}-za+az^{-1}$ (db)

The coefficients of the monomials

t^{r}q^{j}

are shown, along with their alternating sums

\chi

(fixed

j

, alternation over

r

).

-2

-1

0

χ

0

1

-2

1

-4

1

-6

1

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