E-infinity obstruction theory

TL;DR

This paper develops an obstruction theory for E-infinity structures on simplicial operads using a spectral sequence, with broad applications including motivic homotopy theory.

Contribution

It introduces a flexible spectral sequence framework to analyze the existence of E-infinity structures, extending to motivic and classical contexts.

Findings

Spectral sequence converges to the homotopy of E-infinity structures.

Obstruction theory derived from the spectral sequence fringe.

Applicable to motivic homotopy theory and classical ring spectra.

Abstract

The space of E-infinity structures on an simplicial operad C is the limit of a tower of fibrations, so its homotopy is the abutment of a Bousfield-Kan fringed spectral sequence. The spectral sequence begins (under mild restrictions) with the stable cohomotopy of the graded right Gamma-module formed by the homotopy groups of C ; the fringe contains an obstruction theory for the existence of E-infinity structures on C. This formulation is very flexible: applications extend beyond structures on classical ring spectra to examples (in references) in motivic homotopy theory.