# Homotopy transfer and formality

## TL;DR

This paper provides a new proof of a theorem linking n-formality of differential graded algebras to chain-level automorphisms, using homotopy transfer and explicit induction, with applications to arrangements and configuration spaces.

## Contribution

It offers an alternative proof of a key theorem on formality, employing homotopy transfer and explicit methods, and extends results to p-adic coefficients for specific algebraic structures.

## Key findings

- Established formality of dg-algebras from arrangements and configuration spaces with p-adic coefficients.
- Provided a new proof technique using homotopy transfer and inductive killing of higher operations.
- Extended the theorem to different hypotheses and contexts.

## Abstract

In a recent paper, the second author and Joana Cirici proved a theorem that says that given appropriate hypotheses, $n$-formality of a differential graded algebraic structure is equivalent to the existence of a chain-level lift of a homology-level degree twisting automorphism using a unit of multiplicative order at least $n$. Here we give another proof of this result of independent interest and under slightly different hypotheses. 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.