Abstract
We provide an intrinsic description of N-super Riemann surfaces and TN-semirigid surfaces. Semirigid surfaces occur naturally in the description of topological gravity as well as topological supergravity. We show that such surfaces are obtained by an integrable reduction of the structure group of a complex supermanifold. We also discuss the supermoduli spaces of TN-semirigid surfaces and their relation to the moduli spaces of N-super Riemann surfaces.
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