Branched coverings of simply connected manifolds

Abstract

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.

13 pages; v2: small improvements and changes; references added; v3: final version, to appear in Topology and its Applications

References in corpus (3)

• On three-manifolds dominated by circle bundles
• Fundamental classes not representable by products
• On the non-existence of certain branched covers

Cited by in corpus (5)

• Ordering Thurston's geometries by maps of non-zero degree
• Brouwer degree, domination of manifolds, and groups presentable by products
• On actions of tori and quaternionic tori on products of spheres
• Geometric structures in Topology, Geometry, Global Analysis and Dynamics
• Branched covering simply-connected 4-manifolds