Seifert fibrations of lens spaces

Understand

We classify the Seifert fibrations of any given lens space L(p,q).

• We give an algorithmic construction of a Seifert fibration of L(p,q) over the base orbifold S^2(m,n) with the coprime parts of m and n arbitrarily prescribed.
• This algorithm produces all possible Seifert fibrations, and the equivalences between the resulting Seifert fibrations are described completely.
• Also, we show that all Seifert fibrations are equivalent to certain standard models.