Seifert fibered space

A Seifert fibered space is a three-manifold decomposed into circles so that every fiber has a standard fibered solid-torus neighborhood. The quotient is a two-dimensional orbifold, whose cone points correspond to exceptional fibers.

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 actionalso descends and, after dividing by its generic order-two kernel, gives a fibration over $S^2$ with one exceptional fiber of multiplicity three.