Foliations with few non-compact leaves
几何拓扑
2014-10-01 v1
摘要
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].
引用
@article{arxiv.math/0205036,
title = {Foliations with few non-compact leaves},
author = {Elmar Vogt},
journal= {arXiv preprint arXiv:math/0205036},
year = {2014}
}
备注
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-12.abs.html