The Arone-Goodwillie spectral sequence for $\Sigma^{\infty}\Omega^n$ and topological realization at odd primes

TL;DR

This paper uses the Goodwillie spectral sequence to establish conditions under which certain unstable modules over the Steenrod algebra can be realized topologically at odd primes.

Contribution

It introduces a novel application of the Goodwillie spectral sequence to topological realization problems for unstable modules at odd primes.

Findings

Derived new realizability conditions for unstable modules

Connected spectral sequence analysis to topological realization

Enhanced understanding of the Steenrod algebra at odd primes

Abstract

We employ the Goodwillie spectral sequence for the iterated loop space functor in order to provide realizability conditions on certain unstable modules over the Steenrod algebra at an odd prime.