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On Branch Loci in Teichmüller Space

W. J. Harvey
Transactions of the American Mathematical Society
Vol. 153 (Jan., 1971), pp. 387-399
DOI: 10.2307/1995564
Stable URL: http://www.jstor.org/stable/1995564
Page Count: 13
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On Branch Loci in Teichmüller Space
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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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