The centralizer resolution of the 𝐾(2)-local sphere at the prime 2

Abstract

Let G 2 be the Morava stabilizer group at the prime 2. We construct a resolution of the K(2)-local sphere at the prime 2 in terms of certain homotopy fixed point spectra which are closely related to the spectrum of topological modular forms. This resolution is in certain ways analogous to the centralizer resolution of the K(n)-local sphere constructed in [18] if p is an odd prime and n = p − 1.