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

Manifold 

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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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