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Author Buser, Peter ♦ Seppälä, Mika
Source CiteSeerX
Content type Text
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Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Teichm Ller Space ♦ Real Structure ♦ Real Curve ♦ Modulus Space ♦ Dehn Twist ♦ Mapping Class Group ♦ Genus Riemann Surface ♦ Holomorphic Automorphisms ♦ Distinct Antiholomorphic Involution ♦ Corresponding Orientation ♦ Automorphism Group ♦ Simple Fact ♦ Full Group ♦ Antiholomorphic Involution ♦ Topological Compact Genus ♦ Quotient Surface
Abstract An orientation reversing involution of a topological compact genus g; g > 2; surface induces an antiholomorphic involution : T g ! T g of the Teichmüller space of genus g Riemann surfaces. Two such involutions and are conjugate in the mapping class group if and only if the corresponding orientation reversing involutions and of are conjugate in the automorphism group of . This is equivalent to saying that the quotient surfaces =hi and =hi are homeomorphic. Hence the Teichmüller space T g has mg = b 3g+4 2 c distinct antiholomorphic involutions, which are also called real structures of T g ([5]). This result is a simple fact that follows from Royden's theorem ([3]) stating that the the mapping class group is the full group of holomorphic automorphisms of the Teichmüller space(g > 2). Let : T g ! T g and : T g ! T g be two real structures that are not conjugate in the mapping class group. In this paper we construct a rea...
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Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article