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 Teichmuller space has, however, several essentially distinct real structures. The purpose of this note is to describe all real structures of the Teichmuller space T(g,n) of compact Riemann surfaces of genus g punctured at n points.
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