Homotopy transfer and formality

Abstract

In this paper, we prove that, given appropriate hypotheses, n-formality of a differential graded algebraic structure is equivalent to the existence of a chain-level automorphism lifting a degree twisting isomorphism relative to a unit of order greater than n. A similar result with slightly different hypothesis was proved by Joana Cirici and the second author. We use the homotopy transfer theorem and an explicit inductive procedure in order to kill the higher operations. As an application of our result, we prove formality with coefficients in the p-adic integers of certain dg-algebras coming from hyperplane and toric arrangements and configuration spaces.