Branched covering simply connected 4-manifolds (Q6165125)

The paper under review answers Problem \(4.113\) (C) in Kirby's list [\textit{R. Kirby} (ed.), AMS/IP Stud. Adv. Math. 2, 35--473 (1997; Zbl 0888.57014)]: Does every irreducible, simply connected, closed, smooth \(4\)-manifold \(X^4\) have a branched cover which is a symplectic manifold? The authors prove that any closed simply connected smooth \(4\)-manifold is \(16\)-fold branched covered by a product of an orientable surface with the \(2\)-torus, where the construction is natural with respect to spin structures. They also discuss analogous results for other families of \(4\)-manifolds with infinite fundamental groups. For the entire collection see [Zbl 1515.57005].