Derived universal Massey products

TL;DR

This paper introduces a new obstruction in derived operadic cohomology that determines all Massey products on the homology of a differential graded algebra, advancing understanding of algebraic formality.

Contribution

It defines the derived universal Massey product as an obstruction to formality in differential graded algebras over graded operads, linking cohomology and Massey products.

Findings

Defines the derived universal Massey product.

Establishes the obstruction's role in algebraic formality.

Connects Massey products with derived operadic cohomology.

Abstract

We define an obstruction to the formality of a differential graded algebra over a graded operad defined over a commutative ground ring. This obstruction lives in the derived operadic cohomology of the algebra. Moreover, it determines all operadic Massey products induced on the homology algebra, hence the name of derived universal Massey product.