Boundaries of Teichmüller spaces and end-invariants for hyperbolic 3-manifolds
نویسندگان
چکیده
We study two boundaries for the Teichmüller space of a surface Teich(S) due to Bers and Thurston. Each point in Bers’ boundary is a hyperbolic 3-manifold with an associated geodesic lamination on S, its endinvariant, while each point in Thurston’s is a measured geodesic lamination, up to scale. We show that when dimC(Teich(S)) > 1 the end-invariant is not a continuous map to Thurston’s boundary modulo forgetting the measure with the quotient topology. We recover continuity by allowing as limits maximal measurable sub-laminations of Hausdorff limits and enlargements thereof.
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