Asymptotics of foliations and ideal boundaries of pseudo-Anosov flows
Topics in Teichmuller Theory and Kleinian Groups
November 15, 2007 11:00 AM to 12:00 PM
Speakers:
Fenley, Sergio
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Abstract: |
We consider pseudo-Anosov flows in
3-manifolds, so that the flows are homotopically compatible. This
means that no closed orbit is freely homotopic to the inverse of
another orbit. Using only the dynamics we produce a flow ideal bo
undary to the universal cover of the manifold. We show that the action
of the fundament al group G on the flow ideal boundary is a uniform
convergence group. This implies that G is Gromov hyperbolic and that
the action of G on the flow ideal sphere is conjugate to the action of
G on its Gromov ideal boundary. This implies that homotopically
compatible pseudo-Anosov flows are quasigeodesic. This has the
following consequence for asymptotic behavior of foliations : Let F be
a foliation in an aspherical 3-manifold which is R-covered or with one
sided branching - then the foliation satisfies the continuous
extension property. This means that the leaves in the universal
cover extend continuously to the the sphere at infinity. |
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Lecture #12604
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