In this paper we study the equivariant category of finite group actions. We introduce the
basic filtration for the orbit space of the action. In terms of this filtration we give upper and …

The transverse (saturated) Lusternik-Schnirelmann category of foliations, introduced by the
first author, is an invariant of foliated homotopy type with values in $\{1, 2,\ldots,\infty\} $. A …

This is a collection of problems from the theory of foliations and related areas, proposed by
the participants in the conference “Foliations 2012” held in Lodz, Poland during June 25–30 …

We prove that if F is a C1–foliation of a compact manifold M with finite transverse saturated
LS category, cats (M, F)<∞, then F has a compact leaf. In contrast, we show that if F is …

We prove that if F is a foliation of a compact manifold M with all leaves compact
submanifolds, and the transverse saturated category of F is finite, then the leaf space M/F is …

We propose a new homotopy invariant for Lie groupoids which generalizes the classical
Lusternik-Schnirelmann category for topological spaces. We use a bicategorical approach to …

The purpose of this paper is to give lower-bound estimates on the tangential category catτ
(M) of a foliated manifold in terms of cup-length in the associated foliation spectral …

The transverse Lusternik–Schnirelmann category of a foliation is an invariant of foliated
homotopy type. In this paper we show that the category of a Riemannian foliation is infinite if …

S. Hurder and FW Kamber*) i. In this note we propose to study the homotopy groups of B~,
the classifying space of G-foliated microbundles [H~, A foliation F on a manifold X is a G …

This is a collection of problems and related comments concerning the geometry, topology
and classification of smooth foliations. It was prepared in anticipation of the “golden month” …