Abstract
A higher-order de Rham complex dRσ [14] is associated with a commutative algebra A and a sequence of positive integers σ = (σ1σ2... It is called regular if σ is nondecreasing. We extend the algebraic definitions of the Lie derivative and interior product with respect to a derivation of A, to higher-order differential forms. These allow us to prove a generalization of the infinitesimal Stokes formula (also known as the Cartan homotopy formula) for higher regular de Rham complexes. In particular, this implies the homotopy invariance property of higher regular de Rham cohomologies for differentiable manifolds.
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