非单模横向齐次叶

Pub Date : 2020-05-16 DOI:10.5802/aif.3412

E. Mac'ias-Virg'os, P. L. Mart'in-M'endez

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引用次数: 0

摘要

通过计算其类基上同调，给出了紧流形上定义的横向齐次叶理的紧性的充分条件。作为一个应用，我们证明了如果叶形是非单模的，则在$S^1$上的环境流形、叶的闭包或伴生的主束纤维的总空间。

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Non-unimodular transversely homogeneous foliations

We give sufficient conditions for the tautness of a transversely homogenous foliation defined on a compact manifold, by computing its base-like cohomology. As an application, we prove that if the foliation is non-unimodular then either the ambient manifold, the closure of the leaves or the total space of an associated principal bundle fiber over $S^1$.

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