Free Seifert fibered pieces of pseudo-Anosov flows

Free Seifert fibered pieces of pseudo-Anosov flows

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Sergio Fenley, Florida State University
Fine Hall 314

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 (a union of geodesics). The proof uses an associated convergence group theorem, hyperbolic blow ups and models of geodesic flows. This is joint work with Thierry Barbot.