%0 Journal Article
%T Branched coverings of simply connected manifolds
%A Christoforos Neofytidis
%J Mathematics
%D 2012
%I arXiv
%X We construct branched double coverings by certain direct products of manifolds for connected sums of copies of sphere bundles over the 2-sphere. As an application we answer a question of Kotschick and Loeh up to dimension five. More precisely, we show that: (1) every simply connected, closed four-manifold admits a branched double covering by a product of the circle with a connected sum of copies of $S^2 \times S^1$, followed by a collapsing map; (2) every simply connected, closed five-manifold admits a branched double covering by a product of the circle with a connected sum of copies of $S^3 \times S^1$, followed by a map whose degree is determined by the torsion of the second integral homology group of the target.
%U http://arxiv.org/abs/1210.1555v3