Surfaces in Three-manifolds with Hyperbolic Fundamental Group
نویسندگان
چکیده
We show that if a closed irreducible three-manifold with hyperbolic fundamental group contains a surface subgroup satisfying a certain geometric regularity assumption, then the surface is either quasiconvex or a virtual fiber. In the latter case, the manifold is hyperbolic. The regularity condition ensures that we may find algebraic bounds on the surface group which are analogous to the diameter bounds imposed by the presence of pleated surfaces in hyperbolic three-manifolds. The proof is a modification of Bonahon’s proof of geometric tameness for hyperbolic three-manifolds with freely indecomposable fundamental group.
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