Coordinates for Teichmüller spaces of b-groups with torsion

Details Coordinates for Teichmüller spaces of b-groups with torsion Coordinates for Teichmüller spaces of b-groups with torsion

1995-02-15

arxiv.org/abs/math/9502201v1

Annal Acad Scien Fenn A I, 20 (1995) 279-300

Mathematics

Geometric Topology

Plain LaTeX, with Bbb subtituted by bf, 19 pgs, 65 Kb, additional file with 4 figures (2 pgs) in ps form

Scientific paper

In this paper we will use b-groups to construct coordinates for the Teichm\"uller spaces of 2-orbifolds. The main technical tool is the parametrization of triangle groups, which allows us to compute explicitly formul\ae\ for generators of b-groups uniformizing orbifolds. In this way, we obtain a technique to pass from the abstract objects of deformation spaces to concrete calculations with M\"obius transformations. We explore this computational character of our work by finding the expressions of certain classical isomorphisms between Teichm\"uller spaces.

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