Cohomology of supermanifolds (Q5895474)

Since de Rham cohomology of a smooth supermanifold coincides with the usual cohomology of a supporting manifold the authors try to define an adequate cohomology theory. They define a bigraded cohomology group of a supermanifold by means of an (r,s)-dimensional density along an (r,s)- dimensional subsupermanifold. In a forthcoming paper the authors promise to consider the relations between their cohomology theory and the classical one.