Spectral sequences of operad algebras

TL;DR

This paper investigates conditions ensuring that operad actions on the second page of spectral sequences extend through all pages to the limit, in both algebraic and topological contexts.

Contribution

It provides new criteria for operad actions to persist across spectral sequence pages, bridging algebraic and topological frameworks.

Findings

Identifies conditions for operad actions to pass from E^2 to E^r pages

Establishes criteria applicable in algebraic and topological spectral sequences

Ensures operad actions extend to the E^ limit

Abstract

We identify conditions under which it is guaranteed that an action of an operad on the $E^2$ page of a spectral sequence passes to $E^r$ for $r\ge 2$ and hence to the $E^\infty$ page. We consider this question in both the purely algebraic and topological settings.