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Topology/Geometry Seminar

Partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds

Sergio Fenley (Florida State)

Location:  zoom link:
Date & time: Tuesday, 23 March 2021 at 3:50PM - 4:50PM

We analyze partially hyperbolic diffeomorphisms in
hyperbolic 3-manifolds and show that up to iterates
they are either i) discretized Anosov flows, or ii) a
double translation example. Case i) means that there is
a topological Anosov flow in the manifold M so that the
diffeomorphism is a variable time map of this flow. In
particular this implies that the diffeomorphism is
dynamically coherent. We do a further analysis of the
second case and prove geometric properties in a finite
cover and for an iterate. This geometric properties imply that
the center leaves can be obtained by collapsing flow lines
of an associated topological Anosov flow. Together these
results imply that if M^3 hyperbolic admits a partially
hyperbolic diffeomorphism then  it admits an Anosov flow.

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