Seifert fibrations of real projective 3-space
= Seifert fibrations of real projective 3-space
{c}
{title2=$\mathbb{RP}^3$}
The Hopf circle action on $S^3$ descends through the antipodal quotient to a free circle action on $\mathbb{RP}^3$, giving a Seifert fibration over $S^2$ with no exceptional fibers. The weighted action
$$
e^{it}(z_1,z_2)=(e^{it}z_1,e^{3it}z_2)
$$
also descends and, after dividing by its generic order-two kernel, gives a fibration over $S^2$ with one exceptional fiber of multiplicity three.