Foliated corona decompositions

#-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...

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...

Foliated Entropy Rigidity

In this article, we develop a general foliated version of the entropy rigidity theorem and “Real Schwarz Lemma” of Besson, Courtois and Gallot.

LS-categories for foliated manifolds

The Index of Operators on Foliated Bundles

We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of pseudodifferential operators and uses techniques for analizing noncommutative algebras similar to those developed in Algebraic Topology, but in the framework of cyclic cohomology and noncommutative geo...