Transfer of A-infinity structures to projective resolutions

TL;DR

This paper demonstrates how A-infinity algebra structures can be transferred to projective resolutions, ensuring uniqueness up to homotopy under certain conditions, especially over rings that are not fields.

Contribution

It extends classical transfer results of A-infinity structures to projective resolutions over general rings, including the transfer of module structures and strict units.

Findings

Transfer of A-infinity structures is possible to projective resolutions.

Transferred structures are unique up to homotopy under connectedness assumptions.

Results apply over rings that are not fields, broadening classical scope.

Abstract

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