2012/10/31 by Christoforos Neofytidis
Mathematics · #Advanced Operator Algebra Research #Combinatorics #Connected sum #Geometric and Algebraic Topology #Geometry #Great circle #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Mathematics #Product (mathematics) #Pure mathematics #Simply connected space #Torsion (gastropod) #math.AT #math.GT #msc:55M25 #msc:57M05 #msc:57M12
paper · pdf · doi:10.1016/j.topol.2014.10.011
published as Topology Appl. 178 (2014) 360--371 · 13 pages; v2: small improvements and changes; references added; v3: final version, to appear in Topology and its Applications
openalex publication_date 2014/10/23 · arxiv created 2014/11/24 · arxiv updated 2019/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 S2 × S1, 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 S3 × S1, followed by a map whose degree is determined by the torsion of the second integral homology group of the target.