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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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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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