Augmented Teichmuller spaces were introduced in the early 1970s by Lipman Bers. They are obtained by adding Riemann surfaces with nodal singularities to the classical Teichmuller space T. Unlike the space T which has a natural structure of a complex manifold, the augmented space has no complex structure (it is not even locally compact). However, its quotient by any finite index subgroup of the mapping class group has structure of a normal complex space (even of a smooth complex orbifold). This result is important for understanding stringy orbifold cohomology and its generalizations. |
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