Obstruction theory for operadic algebras

Abstract

We study obstruction theory for formality of chain operadic algebras. We construct a canonical class γ_A for an algebra A over a cofibrant chain operad P_∞. This class takes values in the Gamma cohomology groups of the homology algebra H*A and depends only on the homotopy type of the algebra. If the canonical class vanishes then there is a successive obstruction. Further, we give a criterion for when two P_∞-algebras are of the same homotopy type.