On branch loci in Teichmüller space

Harvey, W. J.

doi:10.1090/S0002-9947-1971-0297994-0

On branch loci in Teichmüller space
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by W. J. Harvey PDF

Trans. Amer. Math. Soc. 153 (1971), 387-399 Request permission

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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