Foliations transverse to fibers of a bundle

Plante, J. F.

doi:10.1090/S0002-9939-1974-0331405-X

Foliations transverse to fibers of a bundle
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by J. F. Plante PDF

Proc. Amer. Math. Soc. 42 (1974), 631-635 Request permission

Abstract:

Consider a fiber bundle where the base space and total space are compact, connected, oriented smooth manifolds and the projection map is smooth. It is shown that if the fiber is null-homologous in the total space, then the existence of a foliation of the total space which is transverse to each fiber and such that each leaf has the same dimension as the base implies that the fundamental group of the base space has exponential growth.

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