The restriction on ranks of groups effectively acting on a topological manifold

Let $G$ be a finite group acting effectively on a topological manifold $M$ of dimension $n$. In 1963 L. N. Mann and J. S. Su proved that if $G=(Z/pZ)^k$ and $M$ is compact, then $k$ is bounded above by a constant depending only on $n$ and dimensions of $Z/pZ$-homology groups of $M$. In 2021 B. Csikós, I. Mundet I Riera, L. Puber and E. Szabó proved Mann–Su theorem in general by bounding the rank of $G$ above by a constant depending only on n and ranks of $Z$-homology groups of $M$. In the talk we will discuss the above results.