Abstract
In this paper, we show that discrete torsion phases in string orbifold partition functions, and membrane discrete torsion phases, are topological actions on the simplicial manifolds associated to orbifold group actions. For this purpose, we introduce an integration theory of smooth Deligne cohomology on a general simplicial manifold, and prove that the integration induces a well-defined paring between the smooth Deligne cohomology and the singular cycles.
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