Transfer of A-infinity structures to projective resolutions

Abstract

We show that an A∞-algebra structure can be transferred to a projective resolution of the complex underlying any A∞-algebra. Under certain connectedness assumptions, this transferred structure is unique up to homotopy. In contrast to the classical results on transfer of A∞-structures along homotopy equivalences, our result is of interest when the ground ring is not a field. We prove an analog for A∞-module structures, and both transfer results preserve strict units.