Seifert Manifolds as Circle Manifolds

Abstract

Seifert manifolds play a crucial role in the classification of 3-manifolds, as they occupy six of the eight geometries proposed by Thurston. In this thesis we determine which Seifert manifolds can be given a smooth action from the circle group. We show how the stabilizer groups and orbit space of this circle manifold relate to the Seifert invariants and base space of the Seifert manifold. In particular, we give a smooth circle action to Brieskorn manifolds and spherical space forms and calculate their stabilizer groups. Additionally, we show that the orbit space is an orbifold.