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. In particular the proofs use in essential ways the Z or Z+Z normal subgroups of the fundamental group. These normal subgroups interact with the orbit space of the flow or the leaf spaces of the stable/unstable foliations, producing invariant axes and chains of lozenges, which help force the rigidity. If there is time we discuss the standard form of pseudo-Anosov flows in periodic Seifert fibered pieces. They can be described as neighborhoods of unions of Birkhoff annuli. This is joint work with Thierry Barbot.
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