Foliations transverse to fibers of a bundle

Author:
J. F. Plante

Journal:
Proc. Amer. Math. Soc. **42** (1974), 631-635

MSC:
Primary 57D30

DOI:
https://doi.org/10.1090/S0002-9939-1974-0331405-X

MathSciNet review:
0331405

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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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0331405-X

Keywords:
Foliation,
fiber bundle,
section,
intersection number,
covering projection,
growth function,
asymptotic homology class

Article copyright:
© Copyright 1974
American Mathematical Society