Gamma homology, Lie representations and E ? multiplications

Abstract

We prove that the stable homotopy of any Γ-module F is the homology of a bicomplex Ξ(F), in which the (q−1)st row is the two-sided bar construction ℬ(Lie* q ,Σ q ,F[q]). This gives a natural homotopical cotangent bicomplex for graded commutative algebras, in a form suitable for use in a new obstruction theory for classifying E ∞ ring structures on spectra. The E ∞ structure on certain Lubin-Tate spectra is a corollary.