Topological symmetries of simply-connected four-manifolds and actions of automorphism groups of free groups

Let $M$ be a simply connected closed $4$-manifold. It is proved that any (possibly finite) compact Lie group acting effectively and homologically trivially on $M$ by homeomorphisms is an abelian group of rank at most two. As applications, let $\mathrm{A}\mathrm{u}\mathrm{t}(F_n)$ be the automorphism group of the free group of rank $n\mathrm{.}$ We prove that any group action of $\mathrm{A}\mathrm{u}\mathrm{t}$ $(n\ge 4)$ on $M\mathrm{\ne }{S}^4$ by homologically trivial homeomorphisms factors through $\mathbb{Z}\mathrm{/}2.$ Moreover, any action of $$ $(n\ge 4)$ on $M\mathrm{\ne }{S}^4$ by homeomorphisms is trivial.