A-infinity structures and Massey products

TL;DR

This paper explores the conditions under which higher Massey products in the cohomology of a differential graded algebra can be detected and reconstructed using higher multiplications from $A_$ structures on quasi-isomorphic cohomology.

Contribution

It provides a framework for understanding how higher Massey products relate to $A_$ structures on cohomology, revealing when and how these products can be recovered.

Findings

Higher Massey products can be detected via $A_$ structures.

Conditions for recovering Massey products are established.

The relationship between quasi-isomorphic $A_$ structures and Massey products is clarified.

Abstract

We show how and when it is possible to detect and recover higher Massey products on the cohomology $H$ of a differential graded algebra $A$ with higher multiplications on quasi-isomorphic $A_\infty$ structures on $H$.