Abstract

We 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. In particular this solves Problem 4.113(C) in Kirby’s list. We also discuss analogous results for other families of $4$-manifolds with infinite fundamental groups.

Keywords

Mathematical Subject Classification

Milestones

Authors