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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $2$.


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Additional Information

Bernard Maskit
Affiliation: Department of Mathematics, The University at Stony Brook, Stony Brook, New York 11794-3651
Email: bernie@math.sunysb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04973-4
PII: S 0002-9939(99)04973-4
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