A classical approach to smooth supermanifolds
A differential-geometric approach to supergeometry is considered, in the sense that our objects of study are superalgebra bundles over smooth manifolds. Our definition is not to be confused with Batchelor’s Theorem, for which we provide a direct proof. Rather, our objects are abstract superalgebra bundles, a special case of which are the so-called split supermanifolds constructed from the exterior algebra functor applied to a given vector bundle.
The highlights of this work are the results proving equivalence between our approach and the usual “algebro-geometric” one using ringed spaces, and a supergeometric version of the Flowbox Theorem.