JournalscmhVol. 72 , No. 3DOI 10.1007/s000140050024

On foliated circle bundles over closed orientable 3-manifolds

  • Shigeaki Miyoshi

    Chuo University, Tokyo, Japan
On foliated circle bundles over closed orientable 3-manifolds cover

Abstract

We show that there exists a family of smooth orientable circle bundles over closed orientable 3-manifolds each of which has a codimension-one foliation transverse to the fibres of class C0 but has none of class C3. There arises a necessary condition induced from the Milnor-Wood inequality for the existence of a foliation transverse to the fibres of an orientable circle bundle over a closed orientable 3-manifold. We show that with some exceptions this necessary condition is also sufficient for the existence of a smooth transverse foliation if the base space is a closed Seifert fibred manifold.