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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On branch loci in Teichmüller space


Author: W. J. Harvey
Journal: Trans. Amer. Math. Soc. 153 (1971), 387-399
MSC: Primary 30A60; Secondary 58D15
MathSciNet review: 0297994
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Abstract: The branch locus of the ramified covering of the space of moduli of Fuchsian groups with fixed presentation by the corresponding Teichmüller space is decomposed into a union of Teichmüller spaces, each characterised by a description of the action of the conformal self-mappings admitted by the underlying Riemann surfaces. Equivalence classes of subloci under the action of the modular group are studied, and counted in certain simple cases. One may compute as a result the number of conjugacy classes of elements of prime order in the mapping class group of closed surfaces.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0297994-0
PII: S 0002-9947(1971)0297994-0
Keywords: Teichmüller spaces, Fuchsian groups of first kind, conformal automorphisms of Riemann surfaces, mapping class group
Article copyright: © Copyright 1971 American Mathematical Society