Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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].

30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int