Foliated round surgery of codimension-one foliated manifolds

LS-categories for foliated manifolds

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 ...

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...

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.

#-cobordisms with Foliated Control

We announce a foliated version of Ferry's metric h-cobordism theorem [13]. Let M be a compact Riemarinian manifold and 7 a smooth foliation of M such that the sectional curvatures of the leaves of 7 are zero. There are numbers a > 0 (depending only on dim(M)) and 6 > 0 (depending on M and 7) so that if W is an h-cobordism over M having 6 control in the directions perpendicular to 7 and having a...