Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebras (Q1081904)

A new approach to superdifferentiable functions of Grassmann variables is developed, which avoids ambiguities in odd derivatives. This is used to give an improved definition of supermanifold over a finite-dimensional Grassmann algebra. A natural embedding of supermanifolds over Grassmann algebras with increasing number (L) of generators is developed, and thus a limit as L tends to infinity is possible. A correspondence between graded manifolds and supermanifolds is constructed, extending earlier results.