Homology, Homotopy and Applications

Volume 25 (2023)

Number 1

Derived universal Massey products

Pages: 189 – 218

DOI: https://dx.doi.org/10.4310/HHA.2023.v25.n1.a10


Fernando Muro (Departamento de Álgebra, Facultad de Matemáticas, Universidad de Sevilla, Spain)


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.


operad, algebra, cohomology, formality, minimal model, resolution

2010 Mathematics Subject Classification

13D03, 16E40, 17B56, 55S20

Received 3 September 2021

Received revised 3 February 2022

Accepted 15 February 2022

Published 22 March 2023