Seifert fibrations of lens spaces

TL;DR

This paper provides a complete classification and construction method for Seifert fibrations of lens spaces, detailing how to generate all possible fibrations and their equivalences.

Contribution

It introduces an algorithmic approach to classify and construct all Seifert fibrations of lens spaces, including their equivalence relations.

Findings

All Seifert fibrations are obtainable via the proposed algorithm.

The paper characterizes when two fibrations are equivalent.

Standard models represent all fibrations.

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.