On the Computation of Ainfinity-Maps

Abstract

Starting from a chain contraction (a special chain homotopy equivalence) connecting a differential graded algebra A with a differential 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 component morphisms of the chain contraction, we obtain a simplified version of the existing formulas of the mentioned A∞-maps, reducing the computational cost of computing mn from O(n!2) to O(n!).