On the computation of A∞-maps?

Abstract. Starting from a chain contraction (a special chain homotopy equivalence) connecting a differential graded algebra A with a differen-tial graded module M, the so-called homological perturbation technique “tensor trick ” [8] provides a family of maps, {mi}i≥1, describing an A∞-algebra structure on M derived from the one of algebra on A. In this paper, taking advantage of some annihilation properties of the compo-nent morphisms of the chain contraction, we obtain a simplified version of the existing formulas of the mentioned A∞-maps, reducing the com-putational cost of computing mn from O(n! 2) to O(n!).