Seifert fiber space

A Seifert fiber space is a 3-manifold together with a decomposition as a disjoint union of circles. In other words, it is a ${\displaystyle S^{1}}$-bundle (circle bundle) over a 2-dimensional orbifold. Many 3-manifolds are Seifert fiber spaces, and they account for all compact oriented manifolds in 6 of the 8 Thurston geometries of the geometrization conjecture.