Branched covering simply-connected 4-manifolds

TL;DR

This paper demonstrates that all closed simply-connected smooth 4-manifolds can be represented as 16-fold branched covers of a product of a surface and a 2-torus, providing a natural construction respecting spin structures.

Contribution

It establishes a universal branched covering representation for simply-connected 4-manifolds, solving a problem from Kirby's list and extending to manifolds with infinite fundamental groups.

Findings

All closed simply-connected smooth 4-manifolds are 16-fold branched covers.

Construction respects spin structures.

Results extend to certain 4-manifolds with infinite fundamental groups.

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.