On the May Spectral Sequence at the prime 2

TL;DR

This paper investigates the structure of the May spectral sequence at prime 2, proposing a conjecture about its entire $E_2$ page, proving it in a large subalgebra, and exploring its role in Massey products and differential computations.

Contribution

It introduces a conjecture describing the $E_2$ page of the May spectral sequence at prime 2 and proves it in a significant subalgebra, advancing understanding of its algebraic structure.

Findings

Conjectured the full $E_2$ page structure in terms of generators and relations.

Proved the conjecture within a large subalgebra covering many dimensions.

Computed all $d_2$ differentials for the generators and related them to Adams vanishing line theorem.

Abstract

We make a conjecture about the whole $E_2$ 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 $E_2$ page plays a universal role in the study of Massey products in commutative DGAs. We conjecture that the $E_2$ page is nilpotent free and also prove it in this subalgebra. We compute all the $d_2$ 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.