2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33389We prove that an analog of the exterior differential acts on the space of arbitrary Lagrangians of multidimensional paths on any manifold or supermanifold, thus making this space into a cochain complex. An analog of the Stokes' formula holds. The construction and the proofs are purely geometrical, in terms of the variation of corresponding actions.LaTeX, 4 pagesDifferential Geometrytext