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2002 Foliations with few non-compact leaves
Elmar Vogt
Algebr. Geom. Topol. 2(1): 257-284 (2002). DOI: 10.2140/agt.2002.2.257

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. "Foliations with few non-compact leaves." Algebr. Geom. Topol. 2 (1) 257 - 284, 2002. https://doi.org/10.2140/agt.2002.2.257

Information

Received: 23 July 2001; Revised: 3 April 2002; Accepted: 4 April 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 0989.57017
MathSciNet: MR1917052
Digital Object Identifier: 10.2140/agt.2002.2.257

Subjects:
Primary: 57R30

Rights: Copyright © 2002 Mathematical Sciences Publishers

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