ABSTRACT
The topology of differentiable manifolds has always been related with various geometric objects on them and in particular with operators invariant with respect to the group of diffeomorphisms of the manifold, operators which act in natural bundles. The role of invariance had been appreciated already in XIX century in physics (differential operators invariant with respect to the group of diffeomorphisms preserving a geometric structure are essential both in Maxwell’s laws of electricity and magnetism and in Einstein’s (and Hubert’s) formulation of general relativity). Simultaneously invariance became a topic of conscious interest for mathematicians (the representation theory flourished in works of F. Klein, followed by Lie, Levi-Civita, E.Cartan; it provided with the language and technique adequate to study geometric structures). Our study of invariant differential operators on supermanifolds began in 1976 as a byproduct of attempts to construct an integration theory on supermanifolds similar to the integration theory of differential forms on manifolds.
