Algebraic and Geometric Topology 2 (2002),
paper no. 12, pages 257-284.
Foliations with few non-compact leaves
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].
Non-compact leaves, Seifert fibration, Epstein hierarchy, foliation cycle, suspension foliation
AMS subject classification.
Submitted: 23 July 2001.
(Revised: 3 April 2002.)
Accepted: 4 April 2002.
Published: 16 April 2002.
Notes on file formats
2, Mathematisches Institut, Freie Universitaet Berlin
Arnimallee 3, 14195 Berlin, Germany
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