Foliations with few non-compact leaves

Elmar Vogt

doi:10.2140/agt.2002.2.257

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Foliations with few non-compact leaves

Elmar Vogt

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Abstract

Let F be a foliation of codimension 2 on a compact manifold with at least one non-compact leaf. We show that then F must contain uncountably many non-compact leaves. We prove the same statement for oriented p-dimensional foliations of arbitrary codimension if there exists a closed p form which evaluates positively on every compact leaf. For foliations of codimension 1 on compact manifolds it is known that the union of all non-compact leaves is an open set [A Haefliger, Varietes feuilletes, Ann. Scuola Norm. Sup. Pisa 16 (1962) 367-397].

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Elmar Vogt. 2002-05-04. Foliations with few non-compact leaves. https://doi.org/10.2140/agt.2002.2.257

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