Volume 2, issue 1 (2002)

Download this article
For printing
Recent Issues

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Foliations with few non-compact leaves

Elmar Vogt

Algebraic & Geometric Topology 2 (2002) 257–284

arXiv: math.GT/0205036

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].

Keywords
non-compact leaves, Seifert fibration, Epstein hierarchy, foliation cycle, suspension foliation
Mathematical Subject Classification 2000
Primary: 57R30
References
Forward citations
Publication
Received: 23 July 2001
Revised: 3 April 2002
Accepted: 4 April 2002
Published: 16 April 2002
Authors
Elmar Vogt
2, Mathematisches Institut
Freie Universität Berlin
Arnimallee 3
14195 Berlin
Germany