Pseudo-Anosov flows in toroidal 3-manifolds

Geometry & Topology
Event time: 
Tuesday, January 18, 2011 - 11:30am to Monday, January 17, 2011 - 7:00pm
431 DL
Sergio Fenley
Speaker affiliation: 
Florida State University and Princeton University
Event description: 

We discuss the following rigidity results:
1) A pseudo-Anosov flow in a Seifert fibered manifold is up
to finite covers topologically conjugate to a geodesic flow;
2) A pseudo-Anosov flow in a solv manifold is topologically
conjugate to a suspension Anosov flow. The proofs use
the structure of the fundamental groups in these
manifolds and the topological theory of pseudo-Anosov flows.
If there is time we also describe the interaction of a
pseudo-Anosov flow with possible Seifert fibered pieces in the
torus decomposition: if the fiber is associated to a periodic
orbit of the flow, we produce a standard form for the flow
in the piece using Birkhoff annuli. We also discuss a large
new family of examples of pseudo-Anosov flows in
graph manifolds. This is joint work with Thierry Barbot.