Some Seifert fiber spaces which are boundaries (Q1084712)

Let M be a closed manifold which possesses a Seifert fibration: a fibration with the torus \({\mathbb{R}}^ n/ {\mathbb{Z}}^ n\) as regular fiber and certain exceptional fibers which are flat manifolds (finitely covered by the torus). It is shown that under certain technical conditions M is the boundary of a compact manifold. The given conditions are not necessary conditions but cover various classes of Seifert manifolds, for example flat manifolds (in this case the result had been known before).