JournalscmhVol. 72, No. 3pp. 400–410

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
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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.

Cite this article

Shigeaki Miyoshi, On foliated circle bundles over closed orientable 3-manifolds. Comment. Math. Helv. 72 (1997), no. 3, pp. 400–410

DOI 10.1007/S000140050024