| |
Topics in Teichmuller Theory and Kleinian Groups |
| November 12, 2007 to November 16, 2007 |
| Organized By: Jeff Brock, Ken Bromberg, Richard Canary, Howard Masur, Alan Reid, Maryam Mirzakhani, and John Smillie |
| |
| Parent Programs: |
| Teichmuller Theory and Kleinian Groups |
| |
| Return to Workshop Description |
| |
Asymptotics of foliations and ideal boundaries of pseudo-Anosov flows
Thursday November 15, 2007
11:00AM - 12:00PM
Speakers:
Sergio Fenley
Abstract:
We consider pseudo-Anosov flows in
3-manifolds, so that the flows are homotopically compatible. This
means that no closed orbit is freely homotopic to the inverse of
another orbit. Using only the dynamics we produce a flow ideal bo
undary to the universal cover of the manifold. We show that the action
of the fundament al group G on the flow ideal boundary is a uniform
convergence group. This implies that G is Gromov hyperbolic and that
the action of G on the flow ideal sphere is conjugate to the action of
G on its Gromov ideal boundary. This implies that homotopically
compatible pseudo-Anosov flows are quasigeodesic. This has the
following consequence for asymptotic behavior of foliations : Let F be
a foliation in an aspherical 3-manifold which is R-covered or with one
sided branching - then the foliation satisfies the continuous
extension property. This means that the leaves in the universal
cover extend continuously to the the sphere at infinity.
|
