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Real structures of Teichmüller spaces

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Abstract

The moduli space Xg of compact Riemann surfaces of genus g, g>1, has a canonical antiholomorphic involution. It can easily be defined in terms of complex curves: a point in Xg represented by a curve C is mapped to the point represented by the complex conjugate ¯C of C. In other words, the moduli space has a canonical real structure (cf. Andreotti and Holm [2]). The Teichmüller space has, however, several essentially distinct real structures. The purpose of this note is to describe all real structures of the Teichmüller space T(g,n) of compact Riemann surfaces of genus g punctured at n points.

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  1. Mika Seppälä

    Present address: Department of Mathematics, University of Helsinki, SF-00100, Helsinki 10

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  1. Fakultät für Mathematik, Universität Bielefeld, BRD-4800, Bielefeld 1

    Mika Seppälä

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  1. Mika Seppälä
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Work supported by the EMIL AALTONEN FOUNDATION

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Seppälä, M. Real structures of Teichmüller spaces. Manuscripta Math 40, 79–86 (1982). https://doi.org/10.1007/BF01168236

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  • DOI: https://doi.org/10.1007/BF01168236

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