Topology Seminar: Stable splittings of mapping spaces

In the 1990's, Greg Arone gave a description of the Snaith splitting of spaces of the form $\Omega^m \Sigma^m X$. His method extended to give a kind of functorial filtration of any space of the form Maps(K, X) where K is a finite complex. In good cases, this leads to a stable splitting of these mapping spaces. We will describe Arone's result with an eye toward applying this to other mapping space functors.