Massey Product and Twisted Cohomology of A-infinity Algebras

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.

32 pages

References in corpus (3)

• Cohomology $C_{\infty }$-algebra and Rational Homotopy Type
• On a spectral sequence for twisted cohomologies
• A twisted tale of cochains and connections

Cited by in corpus (1)

• A-infinity algebras associated with curves and rational functions on M_{g,g}. I