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Parametrization of Teichmüller spaces by geodesic length functions

  • Mika Seppälä
  • Tuomas Sorvali
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 11)

Abstract

The Teichmüller space T(Σ) of a compact C -surface Σ can be parametrized by geodesic length functions. More precisely, we can find a set {α1... ,α n} of closed curves α j on Σ such that the isotopy class of a hyperbolic metric d on Σ (i.e. the point [d] ∊ T(Σ)) is determined by the lengths of geodesic curves homotopic to the curves α j on (Σ, d). However, since the fundamental group of Σ is not freely generated there is a quite complicated relation among these geodesic length function.

Keywords

Riemann Surface Fundamental Group Common Fixed Point Closed Curf Fuchsian Group 
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 New York Inc. 1988

Authors and Affiliations

  • Mika Seppälä
    • 1
    • 2
  • Tuomas Sorvali
    • 3
  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgDeutschland
  2. 2.Department of MathematicsUniversity of HelsinkiHelsinkiFinland
  3. 3.Department of MathematicsUniversity of JoensuuJoensuuFinland

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