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New parameters for Fuchsian groups of genus $2$

Author: Bernard Maskit
Journal: Proc. Amer. Math. Soc. 127 (1999), 3643-3652
MSC (1991): Primary 30F10; Secondary 32G15
Published electronically: May 13, 1999
MathSciNet review: 1616641
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Abstract: 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 $2$.

References [Enhancements On Off] (What's this?)

  • 1. J. Gilman and B. Maskit. An algorithm for 2-generator fuchsian groups. Mich. Math. J., 38:13-32, 1991. MR 92f:30062
  • 2. A. Haas and P. Susskind. The geometry of the hyperelliptic involution in genus two. Proc. Amer. Math. Soc., 105:159-165, 1989. MR 89e:30078
  • 3. B. Maskit. Explicit matrices for fuchsian groups. Cont. Math., 169:451-466, 1994. MR 96f:30045
  • 4. B. Maskit. A picture of moduli space. Invent. math., 126:341-390, 1996. MR 97m:32034

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Additional Information

Bernard Maskit
Affiliation: Department of Mathematics, The University at Stony Brook, Stony Brook, New York 11794-3651

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
Article copyright: © Copyright 1999 American Mathematical Society

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