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Title:
Body and soul decompositions in supergeometry
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Abstract:
Given a supermanifold with a projection map to the reduced manifold, elements of the structure sheaf decompose into a ``body'', a function on the reduced manifold, and a complementary part called the ``soul''. This induces, in turn, a decomposition of various kinds of geometric structure one could put on a supermanifold, including de Rham forms, line bundles with connection, as well as higher degree classes in Deligne cohomology.
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