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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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New parameters for Fuchsian groups of genus $2$
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by Bernard Maskit PDF
Proc. Amer. Math. Soc. 127 (1999), 3643-3652 Request permission


We give a new real-analytic embedding of the Teichmüller space of closed Riemann surfaces of genus 2 into ${\mathbb R^6}$. The parameters are explicitly defined in terms of the underlying hyperbolic geometry. The embedding is accomplished by writing down four matrices in $PSL(2,{\mathbb R})$, where the entries in these matrices are explicit algebraic functions of the parameters. Explicit inequalities are given to define the image of the embedding; the four matrices corresponding to a point in this image generate a fuchsian group representing a closed Riemann surface of genus $2$.
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Additional Information
  • Bernard Maskit
  • Affiliation: Department of Mathematics, The University at Stony Brook, Stony Brook, New York 11794-3651
  • Email:
  • Received by editor(s): October 20, 1997
  • Received by editor(s) in revised form: February 20, 1998
  • Published electronically: May 13, 1999
  • Additional Notes: Research supported in part by NSF Grant DMS 9500557.
  • Communicated by: Albert Baernstein II
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3643-3652
  • MSC (1991): Primary 30F10; Secondary 32G15
  • DOI:
  • MathSciNet review: 1616641