On foliated circle bundles over closed orientable 3-manifolds | Zendy

Shigeaki Miyoshi | Zendy

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On foliated circle bundles over closed orientable 3-manifolds

Author(s) -

Shigeaki Miyoshi

Publication year - 1997

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050024

Subject(s) - fibered knot , foliation (geology) , mathematics , codimension , pure mathematics , manifold (fluid mechanics) , transverse plane , bundle , base (topology) , mathematical analysis , anatomy , geology , mechanical engineering , medicine , materials science , geochemistry , engineering , metamorphic rock , composite material

. 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 C 0 but has none of class C 3 . 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.

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