Seifert fibrations of lens spaces

Abstract

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.