Quasigeodesic Flows and Sphere-filling Curves
نویسنده
چکیده
Given a closed hyperbolic 3-manifold M with a quasigeodesic flow we construct a π1-equivariant sphere-filling curve in the boundary of hyperbolic space. Specifically, we show that any complete transversal P to the lifted flow on H3 has a natural compactification as a closed disc that inherits a π1 action. The embedding P →֒ H3 extends continuously to the compactification and the restriction S1 → S2 ∞ to the boundary is a surjective π1-equivariant map. This generalizes the result of Cannon and Thurston for fibered hyperbolic 3-manifolds.
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