Broken hyperbolic structures and affine foliations on surfaces |
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Authors: | Ulrich Oertel |
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Institution: | a Department of Mathematics, Rutgers University, NJ 07102, USA b Institut de Mathématiques, CNRS and Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg Cedex, France |
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Abstract: | In this paper, we introduce two new kinds of structures on a non-compact surface: broken hyperbolic structures and broken measured foliations. The space of broken hyperbolic structures contains the Teichmüller space of the surface as a subspace. The space of broken measured foliations is naturally identified with the space of affine foliations of the surface. We describe a topology on the union of the space of broken hyperbolic structures and of the space of broken measured foliations which generalizes Thurston's compactification of Teichmüller space. |
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