The Teichmuller space T_g is the space of marked Riemann surfaces, i.e. complex structures on a closed orientable surface of genus g modulo homeomorphisms isotopic to the identity. The augmented Teichmuller space, introduced by Lipman Bers, is obtained by adding to T_g Riemann surfaces with nodal singularities. Unlike the space T which has a natural structure of a complex manifold, the augmented Teichmuller 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 a structure of a normal complex space (even of a smooth complex orbifold). This result is important for understanding cup-product in stringy orbifold cohomology and its generalizations. |