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Quasigeodesic pseudo-Anosov flows

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Sergio Fenley (Princeton/Florida State University)

Abstract: A quasigeodesic is a curve which is uniformly efficient
in measuring distances in relative homotopy classes or equivalently
efficient up to a bounded multiplicative distortion in measuring distances when lifted to the universal cover. A flow is quasigeodesic if all flow lines are quasigeodesics.
The talk will explore quasigeodesic pseudo-Anosov flows in atoroidal 3-manifolds, of which there are several infinite
families of examples. By geometrization and irreducibility
the manifolds are hyperbolic. In such manifolds quasigeodesics
are extremely important as for instance they are a bounded
distance from minimal geodesics (in the universal cover).
One important result is that such flows induce ideal maps from the ideal boundary of the stable/unstable leaves to the boundary of hyperbolic 3-space. The talk will also explore properties of these maps and in particular identification of ideal points.
This is connected with the property of the stable/unstable
foliations being quasi-isometric foliations.
The tools are the dynamics of the flow and also
the large scale geometry of the universal cover.