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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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Keywords: Teichmüller spaces, Fuchsian groups of first kind, conformal automorphisms of Riemann surfaces, mapping class group
Article copyright: © Copyright 1971 American Mathematical Society