On fibering certain foliated manifolds overS1

LS-categories for foliated manifolds

The rank of the fundamental group of certain hyperbolic 3–manifolds fibering over the circle

Probably the most basic invariant of a finitely generated group is its rank, ie the minimal number of elements needed to generate it. In general the rank of a group is not computable. For instance, there are examples, due to Baumslag, Miller and Short [3], of hyperbolics groups showing that there is no uniform algorithm solving the rank problem. Everything changes in the setting of 3–manifold g...

On fibering and splitting of 5-manifolds over the circle

Our main result is a generalization of Cappell’s 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the smoothable splitting and fibering problems for certain 5-manifolds mapping to the circle. For example, these maps may have homotopy fibers which are in the class of finite connected sums of certain geometric 4-manifolds. Most of these homotopy fibers h...

Functional calculus for tangentially elliptic operators on foliated manifolds ∗

3 Pseudodifferential functional calculus 7 3.1 Complex powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Action in Sobolev spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 f(A) as pseudodifferential operators . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 The case of Finsler foliations . . . . . . . . . . . . ...

The Index of Hypoelliptic Operators on Foliated Manifolds

In [EE1] and [EE2] we presented the solution to the index problem for a natural class of hypoelliptic differential operators on compact contact manifolds. The methods developed to deal with that problem have wider applicability to the index theory of hypoelliptic Fredholm operators. As an example of the power of the proof techniques we present here a new proof of a little known index theorem of...