Geodesic
Foliations with few non-compact leaves
Vogt, Elmar1
12, Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany
Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 257-284
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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].

DOI : 10.2140/agt.2002.2.257
Keywords: non-compact leaves, Seifert fibration, Epstein hierarchy, foliation cycle, suspension foliation

Vogt, Elmar  1

1 2, Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany 
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Vogt, Elmar. Foliations with few non-compact leaves. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 257-284. doi: 10.2140/agt.2002.2.257

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