Uniqueness of MoravaK-theory

Abstract

AbstractWe show that there is an essentially uniqueS-algebra structure on the MoravaK-theory spectrumK(n), whileK(n) has uncountably manyMUor$\widehat {E(n)}$-algebra structures. Here$\widehat {E(n)}$is theK(n)-localized Johnson–Wilson spectrum. To prove this we set up a spectral sequence computing the homotopy groups of the moduli space ofA∞structures on a spectrum, and use the theory ofS-algebrak-invariants for connectiveS-algebras found in the work of Dugger and Shipley [Postnikov extensions of ring spectra, Algebr. Geom. Topol.6(2006), 1785–1829 (electronic)] to show that all the uniqueness obstructions are hit by differentials.