Seifert fiber space

Summary

A Seifert fiber space is a 3-manifold decomposed into disjoint circles, called fibers, that fit together locally like a standard fibered solid torus. Almost all fibers are regular, and around each of the finitely many exceptional fibers the nearby fibers wind several times. The space of fibers is a $2$-dimensional orbifold, and the manifold is classified by this base and a few integer invariants. Seifert fiber spaces account for six of the eight Thurston geometries and are one of the two kinds of pieces in the JSJ decomposition.