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Topology/Geometry Seminar

Partial hyperbolicity and pseudo-Anosov dynamics (Cancelled)

Sergio Fenley (Florida State)

Location:  Hill 705
Date & time: Tuesday, 18 February 2020 at 3:50PM - 4:40PM

We study partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds. We classify these diffeomorphisms and obtain results concerning the global structure of these diffeomorphisms in these manifolds.  We announce preliminaries results showing the following: up to finite iterates, if a partially hyperbolic diffeomorphism of a hyperbolic 3-manifold is not leaf conjugate to the time one map of a topological Anosov flow, then it can be obtained as a blow down of a power of a "step up" map of an R-covered topological Anosov flow. In particular this shows that a hyperbolic 3-manifold that admits a partially hyperbolic diffeomorphism also admits a topological Anosov flow. Very similar techniques can be used to prove that if a partially hyperbolic diffeomorphism of a Seifert fibered spaces induces a pseudo-Anosov diffeomorphism in the base surface, then it is not dynamically coherent, and it is also obtained by an appropriate blow down of a smooth R-covered Anosov flow.