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manuscripta mathematica

, Volume 104, Issue 3, pp 383–406 | Cite as

Affine foliations and covering hyperbolic structures

  • Ulrich Oertel
  • Athanase Papadopoulos

Abstract:

We describe the relationship between closed affine laminations in a punctured surface and some associated hyperbolic structures on certain covers of the punctured surface, which we call covering hyperbolic structures. Further, in analogy with the theory of William Thurston relating the Teichmüller space of a surface to the projective lamination space, we describe a space with points representing affine laminations in a given surface and with other points representing the associated covering hyperbolic structures.

Mathematics Subject Classification (2000): 57M50, 32G15, 30F60, 57R30, 57M10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ulrich Oertel
    • 1
  • Athanase Papadopoulos
    • 2
  1. 1.Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, USA. e-mail: oertel@andromeda.rutgers.eduUS
  2. 2.Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France.¶e-mail: papadop@math.u-strasbg.frFR

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