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Hyperbolic Manifolds and the Compact Two-dimensional Case

  • Riccardo Benedetti
  • Carlo Petronio
Part of the Universitext book series (UTX)

Abstract

In this chapter we are going to introduce the notion of hyperbolic manifold (i.e. a manifold modeled on hyperbolic space) via the introduction of a much more general class of manifolds. We shall prove the first essential properties of such manifolds (namely, the fact that if a hyperbolic manifold is complete then it can be obtained as a quotient of hyperbolic space). Afterwards we shall consider the special case of compact surfaces and we shall give a complete classification of the hyperbolic structures on a surface of fixed genus (that is we shall give a parametrization of the so-called Teichmüller space).

Keywords

Conjugacy Class Hyperbolic Space Hyperbolic Manifold Isotopy Class Hyperbolic Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Riccardo Benedetti
    • 1
  • Carlo Petronio
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di PisaPisaItaly

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