Augmented Teichmuller Spaces and Orbifolds

Details Augmented Teichmuller Spaces and Orbifolds Augmented Teichmuller Spaces and Orbifolds

2007-05-20

arxiv.org/abs/0705.2859v4

Mathematics

Complex Variables

92 pages; rewritten introduction, improved exposition; accepted for publication in Selecta Mathematica. A gap in the proof of

Scientific paper

We study complex-analytic properties of the augmented Teichmuller spaces ATS introduced by Lipman Bers. These spaces are obtained by adding to the classical Teichmuller space TS the points corresponding to nodal Riemann surfaces. Unlike TS, the space ATS is not a complex manifold (it is not even locally compact). We prove however that the quotient of ATS by any finite index subgroup of the Teichmuller modular group has a canonical structure of a complex orbifold. Using this structure we construct natural maps from ATS to stacks of admissible coverings of stable Riemann surfaces. This result is important for understanding the cup-product in stringy orbifold cohomology. We also establish some new technical results from the general theory of orbifolds which may be of independent interest.

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