Behavior of geodesics in foliated manifolds with bundle-like metrics

Hodge Cohomology of Some Foliated Boundary and Foliated Cusp Metrics

For fibred boundary and fibred cusp metrics, Hausel, Hunsicker, and Mazzeo identified the space of L harmonic forms of fixed degree with the images of maps between intersection cohomology groups of an associated stratified space obtained by collapsing the fibres of the fibration at infinity onto its base. In the present paper, we obtain a generalization of this result to situations where, rathe...

LS-categories for foliated manifolds

Geodesics in Riemannian Manifolds with Boundary

Many problems arising in practical situations have boundary constraints and can only be described in the setting of Riemannian manifolds with boundary. This justifies our focus in this report on various geometric aspects of manifolds with boundary. In particular, we are interested in those results concerning the properties of geodesics in such manifolds. A related problem is the geometry of wav...

Transverse Lusternik{Schnirelmann category of foliated manifolds

The purpose of this paper is to develop a transverse notion of Lusternik{Schnirelmann category in the eld of foliations. Our transverse category, denoted cat\j (M;F), is an invariant of the foliated homotopy type which is nite on compact manifolds. It coincides with the classical notion when the foliation is by points. We prove that for any foliated manifold catM catL cat\j (M;F), where L is a ...

Tautly foliated 3-manifolds with no R-covered foliations

We provide a family of examples of graph manifolds which admit taut foliations, but no R-covered foliations. We also show that, with very few exceptions, R-covered foliations are taut.