On finite simple and nonsolvable groups acting on homology 4-spheres (Q2502946)

The paper under review studies actions of finite simple and nonsolvable groups on homology 4-spheres. All actions are assumed to be smooth, effective and orientation-preserving. The main result is that the only finite simple groups acting on a homology 4-sphere are the alternating or linear fractional groups \({\mathbb A}_5\cong\text{PSL}(2,5)\) and \({\mathbb A}_6\cong \text{PSL}(2,9)\). Furthermore, applying this gives a list of groups which contains all finite nonsolvable groups admitting an action on a homology 4-sphere.