Abstract:
Given a differential graded algebra (dga) C and three cohomology classes a, b, c in H(C), we can define the triple Massey product <a, b, c> as long as ab=bc=0. We can consider the graded algebra F_2[a, b, c]/(ab, bc), a commutative F_2-algebra where we have precisely the relations for the Massey product <a, b, c> to be defined. For a dga with cohomology ring F_2[a, b, c]/(ab, bc), there are a priori two options for <a, b, c>, either it vanishes or not. It turns out that only the first option can occur, the nonvanishing product cannot be realized. In the talk, I will try to sketch a proof of this result. To do this, I will introduce the concepts of Massey products, Hochschild cohomology and A_∞-algebras and explain how they relate to each other.