Tight contact structures and taut foliations.
Let be a closed, foliated manifold, and let be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which admits an approximating (Tischler) fibration over . If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.
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,...