Formes différentielles pour les algèbres sur une opérade

Abstract

In this Note we extend the notions of cochains theory and simplicial forms, which have been developed in rational homotopy theory, to algebras over an operad. We define a notion of simplicial homotopy for this type of algebras. We also construct a simplicial forms functor for E ∞-algebras. After Mandell's recent results we know that they give algebraic models for p-adic homotopy. This functor is analogous to the Sullivan's simplical commutative differential forms functor.