E2 formality via obstruction theory

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.

18 pages

References in corpus (14)

• Combinatorial operad actions on cochains
• Moment-angle complexes, monomial ideals, and Massey products
• Topological Hochschild homology of Thom spectra and the free loop space
• On Davis-Januszkiewicz homotopy types I; formality and rationalisation
• Lifting homotopy T-algebra maps to strict maps
• Etale cohomology, purity and formality with torsion coefficients
• Non-commutative formality implies commutative and Lie formality
• Behavior of Quillen (co)homology with respect to adjunctions
• Homotopy Gerstenhaber algebras are strongly homotopy commutative
• Homotopy Gerstenhaber formality of Davis-Januszkiewicz spaces
• The cohomology of biquotients via a product on the two-sided bar construction
• Quillen (co)homology of divided power algebras over an operad
• An obstruction theory for strictly commutative algebras in positive characteristic
• Kaledin classes and formality criteria