## Topology & Geometric Group Theory Seminar

## Fall 2011

### 1:30 – 2:30, Malott 203

### Thursday, November 10

**Sergio Fenley**,
Florida State University

*Pseudo-Anosov flows in Seifert fibered and solvable 3-manifolds*

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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