The Bers-Greenberg Theorem and the Maskit Embedding for Teichmüller spaces

Details The Bers-Greenberg Theorem and the Maskit Embedding for Teichmüller spaces The Bers-Greenberg Theorem and the Maskit Embedding for Teichmüller spaces

1995-01-22

arxiv.org/abs/math/9501202v1

Mathematics

Geometric Topology

15 pages, plain LaTeX, bf for Bbb, 2 figures in plain LaTeX, hard copies available under request

Scientific paper

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

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