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Branched covering simply connected 4-manifolds

### David Auckly, R. İnanç Baykur, Roger Casals, Sudipta Kolay, Tye Lidman and Daniele Zuddas

Vol. 5 (2022), No. 1, 31–42
##### 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
branched cover, 4-manifold, symplectic
##### Mathematical Subject Classification
Primary: 57K40, 57M12