On the May spectral sequence at the prime 2

Abstract

We make a conjecture about the whole E2 page of the May spectral sequence in terms of generators and relations and we prove it in a subalgebra which covers a large range of dimensions. We show that the E2 page plays a universal role in the study of Massey products in commutative DGAs. We conjecture that the E2 page is nilpotent free and also prove it in this subalgebra. We compute all the d2 differentials of the generators in the conjecture and construct maps of spectral sequences which allow us to explore Adams vanishing line theorem to compute differentials in the May spectral sequence.