Obstructions for Associativity in Stable Homotopy Theory

Abstract

We give a construction of the obstruction theory for ${\mathbb{A}}_n$-algebra structures in stable $\infty$-categories, and give some properties of it. We use this to show that the spectrum $\mathbb{S}/4$ admits an ${\mathbb{A}}_5$-multiplication using synthetic spectra.

25 pages, 4 figures