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15 February 2001 Boundaries of Teichmüller spaces and end-invariants for hyperbolic 3-manifolds
Jeffrey F. Brock
Duke Math. J. 106(3): 527-552 (15 February 2001). DOI: 10.1215/S0012-7094-01-10634-0

Abstract

We study two boundaries for the Teichmüller space of a surface Teich(S) due to L. Bers and W. Thurston. Each point in Bers's boundary is a hyperbolic 3-manifold with an associated geodesic lamination on S, its end-invariant, while each point in Thurston's is a measured geodesic lamination, up to scale. When dim(Teich(S))>1, we show that 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 sublaminations of Hausdorff limits and enlargements thereof.

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Jeffrey F. Brock. "Boundaries of Teichmüller spaces and end-invariants for hyperbolic 3-manifolds." Duke Math. J. 106 (3) 527 - 552, 15 February 2001. https://doi.org/10.1215/S0012-7094-01-10634-0

Information

Published: 15 February 2001
First available in Project Euclid: 13 August 2004

zbMATH: 1011.30042
MathSciNet: MR1813235
Digital Object Identifier: 10.1215/S0012-7094-01-10634-0

Subjects:
Primary: 30F60
Secondary: 30F45, 37F30, 57M50

Rights: Copyright © 2001 Duke University Press

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Vol.106 • No. 3 • 15 February 2001
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