Group actions and the topology of nonnegatively curved 4-manifolds (Q1362383)

The author studies topological properties of nonnegatively curved (compact) 4-manifolds \(M\) which admit effective isometric actions by finite groups. The first theorem of the paper states that if \(M\) has a \((\mathbb{Z}_p \times \mathbb{Z}_p)\)-action for \(p\) prime and large enough, then the Euler-Poincaré characteristic of \(M\) is less than or equal to 5. The second theorem requires no hypothesis on the structure of the isometry group of \(M\) other than it be large, but it does require \(M\) to be \(\delta\)-pinched. More precisely, for every \(\delta >0\) there exists a positive integer \(N= N(\delta)\) such that if the sectional curvature of \(M\) belongs to \([\delta,1]\), and \(|\text{Isom} (M) |>N\), then \(\chi (M)\leq 3\).