Some remarks on the differential-geometric approach to supermanifolds (Q1111207)

The authors provide an analysis of the category of \(GH^{\infty}\) supermanifolds introduced by \textit{A. Rogers} [Commun. Math. Phys. 105, 375-384 (1986; Zbl 0602.58005)]. They show that a natural definition of vector bundle is not possible in this category. On the other hand, they show that any \(GH^{\infty}\) supermanifold can be made into a supermanifold of a new category which is well-behaved and which is a supermanifold in the sense of M. Rothstein.