E2 formality via obstruction theory

TL;DR

This paper investigates the E_2-formality of differential graded algebras over prime fields using obstruction theory, establishing formality for certain classes and applications to classifying spaces.

Contribution

It introduces a novel obstruction-theoretic approach to prove E_2-formality for specific algebraic and topological structures.

Findings

E_2-algebras with polynomial cohomology on even degree classes are intrinsically formal.

Proved E_2-formality of classifying spaces of some compact Lie groups.

Established E_2-formality of Davis-Januszkiewicz spaces.

Abstract

We attack the question of E_2-formality of differential graded algebras over prime fields via obstruction theory. We are able to prove that E_2-algebras whose cohomology ring is a polynomial algebra on even degree classes are intrinsically formal. As a consequence we prove E_2-formality of the classifying space of some compact Lie group or of Davis-Januszkiewicz spaces.