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Topology/Geometry Seminar

Free Seifert fibered pieces of pseudo-Anosov flows

Dr. Sergio Fenley: Florida State University and Princeton University

Location:  Hill 005
Date & time: Tuesday, 14 February 2017 at 3:30PM - 3:31PM

We prove a structure theorem for pseudo-Anosov flows restricted to Seifert fibered pieces of three manifolds. The piece is called periodic if there is a Seifert fibration so that a regular fiber is freely homotopic, up to powers, to a closed orbit of the flow. A non periodic Seifert fibered piece is called free. In this talk we consider free Seifert pieces. We show that, in a carefully defined neighborhood of the free piece, the pseudo-Anosov flow is orbitally equivalent to a hyperbolic blow up of a geodesic flow piece. A geodesic flow piece is a finite cover of the geodesic flow on a compact hyperbolic surface, usually with boundary. We introduce almost k-convergence groups, and an associated convergence theorem. We also introduce an alternative model for the geodesic flow of a hyperbolic surface that is suitable to prove these results, and we define what is a hyperbolic blow up.

This is joint work with Thierry Barbot.

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Department of Mathematics

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Rutgers University
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