In this paper we characterize manifolds (topological or smooth, compact or not, with or without boundary) which admit flows having a dense orbit (such manifolds and flows are called transitive) thus fully answering some questions by Smith and Thomas. Name
The Hausdorff dimension of the holonomy pseudogroup of a codimension-one foliation ℱ is shown to coincide with the Hausdorff dimension of the space of compact leaves (traced on a complete transversal) when ℱ is non-minimal, and to be equal to zero when ℱ is minimal with non-trivial leaf holonomy.
A foliation of a manifold is transversely homogeneous if it can be defined by local submersions to a homogeneous space which on overlaps differ by translations. We explore the topology and geometry of such foliations and give a structure theorem for the case when is compact. We investigate the relationship between the structure equations of and the normal bundle of the foliation and provide a differential forms characterization of a large class of homogeneous foliations. As a special case,...