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Journal of the London Mathematical Society 1997 55(3):558-568; doi:10.1112/S002461079700519X
© 1997 by London Mathematical Society
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© The London Mathematical Society

The Bers–Greenberg Theorem and the Maskit Embedding for Teichmüller Spaces

Pablo Arés Gastesi

Mathematics Department, SUNY at Stony Brook, USA and School of Mathematics, Tata Institute of Fundamental Research Bombay, India. E-mail: pablo{at}motive.math.tifr.res.in

Received 6 May 1994. Revision received 10 March 1995.

The Bers–Greenberg theorem tells us that the Teichmüller space of a Riemann surface with branch points (orbifold) depends only on the genus and the number of special points, and not on the particular ramification values. On the other hand, the Maskit embedding provides a mapping from the Teichmüller space of an orbifold, into the product of one-dimensional Teichmüller spaces. In this paper we prove that there is a set of isomorphisms between one-dimensional Teichmüller spaces that, when restricted to the image of the Teichmüller space of an orbifold under the Maskit embedding, provides the Bers–Greenberg isomorphism.


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