  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 $\mathrm{Aut}(F_{n})$ be the automorphism group of the free
group of rank $n.$ We prove that any group action of $\mathrm{Aut}% (F_{n})$
$(n\geq 4)$ on $M\neq S^{4}$ by homologically trivial homeomorphisms factors
through $\mathbb{Z}/2.$ Moreover, any action of $% \mathrm{SL}_{n}(\mathbb{Q})$
$(n\geq 4)$ on $M\neq S^{4}$ by homeomorphisms is trivial.
