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A combination theorem for Veech subgroups of the mapping class group. (English) Zbl 1099.57002
Veech groups are remarkable subgroups of the mapping class group which act as lattices on holomorphic discs. However they are never cocompact, and hence do not provide subgroups of the mapping class group which are isomorphic to the fundamental groups of closed surfaces. The present paper adapts the Klein combination theorem to combine two Veech groups along a common cyclic subgroup consisting of parabolics to construct a closed surface group inside the mapping class group. All but one conjugacy class in this subgroup consists of hyperbolic (pseudo-Anosov) mapping classes. The paper is very well written and explains the background necessary for these constructions very clearly.

MSC:
57M07 Topological methods in group theory
30F60 Teichmüller theory for Riemann surfaces
20F65 Geometric group theory
57M99 General low-dimensional topology
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