Let $F$ be a foliation which is almost transverse

to a pseudo-Anosov flow $A$ in a closed 3-manifold with

negatively curved fundamental group. Suppose that $A$

is a quasigeodesic flow. We prove that in the

universal cover, the lifted leaves of $\tilde F$ extend continuously

to the sphere at infinity, giving a continuous

parametrization of their limit sets. This applies for

instance to every Reebless finite depth foliation

in hyperbolic 3-manifolds, which exist whenever

the second Betti number is non zero. It also applies

to large classes of foliations with all leaves dense

and to infinitely many foliations with one sided

branching. One important tool is a careful analysis

of one dimensional singular foliations induced

in the leaves of $F$ or $\tilde F$ by the stable/unstable

singular foliations of the flow $A$.

# Asymptotic behavior of foliations

Event time:

Thursday, March 3, 2005 - 11:30am to Wednesday, March 2, 2005 - 7:00pm

Location:

431 DL

Speaker:

Sergio Fenley

Speaker affiliation:

Florida State University

Event description: