Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular riemannian foliations on simply connected spaces   A singular riemannian foliation on a complete riemannian manifold is said to
be riemannian if each geodesic that is perpendicular at one point to a leaf
remains perpendicular to every leaf it meets. The singular foliation is said to
admit sections if each regular point is contained in a totally geodesic
complete immersed submanifold that meets every leaf orthogonally and whose
dimension is the codimension of the regular leaves. A typical example of such
singular foliation is the partition by orbits of a polar action,e.g. the orbits
of the adjoint action of a compact Lie group on itself.
  We prove that a singular riemannian foliation with compact leaves that admit
sections on a simply connected space has no exceptional leaves, i.e., each
regular leaf has trivial normal holonomy. We also prove that there exists a
convex fundamental domain in each section of the foliation and in particular
that the space of leaves is a convex Coxeter orbifold.

3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex