Massey Product and Twisted Cohomology of A-infinity Algebras

TL;DR

This paper explores the structure of twisted cohomology in $A_infty$-algebras, introducing higher Massey products, and demonstrates their naturality and relation to spectral sequences.

Contribution

It defines higher Massey products on $A_infty$-algebra cohomology and shows their naturality and connection to spectral sequence differentials.

Findings

Higher Massey products are defined on $A_infty$-algebra cohomology.

Spectral sequence converges to twisted cohomology with differentials given by Massey products.

Naturality of constructions under morphisms and homotopies is established.

Abstract

We study the twisted cohomology groups of $A_\infty$-algebras defined by twisting elements and their behavior under morphisms and homotopies using the bar construction. We define higher Massey products on the cohomology groups of general $A_\infty$-algebras and establish the naturality under morphisms and their dependency on defining systems. The above constructions are also considered for $C_\infty$-algebras. We construct a spectral sequence converging to the twisted cohomology groups an show that the higher differentials are given by the $A_\infty$-algebraic Massey products.