Let M be a manifold with a fiber bundle E which is a modulus over the exterior forms. An exterior connection is defined by the formulas:
(α∧β).s=α.(β.s)
∇(α.s)=dα.s+(−1)deg(α)α.∇(s)
with α,β∈Λ∗(TM), and s a section of E. The curvature is R=∇∘∇ such that:
R(α.s)=α.R(s)
Can we make differential geometry with the exterior connections?