2020/04/27 by Alejandro Cañas, Vicente Muñoz, Cañas, A. +5
Mathematics · #14J17 #14J28 #53C25 #53D35 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2004.12643
openalex publication_date 2020/04/27 · openalex created_date 2020/05/01 · openalex updated_date 2026/07/28
Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact structures are obtained mainly by two techniques. These are either links (Boyer and Galicki), or semi-regular Seifert fibrations over smooth orbifolds (Kollár). Recently, the second named author of this article started the systematic development of quasi-regular Seifert fibrations, that is, over orbifolds which are not necessarily smooth. The present work is devoted to several applications of this theory. First, we develop constructions of a Smale-Barden manifold admitting a quasi-regular Sasakian structure but not a semi-regular K-contact structure. Second, we determine all Smale-Barden manifolds that admit a null Sasakian structure. Finally, we show a counterexample in the realm of cyclic Kähler orbifolds to the algebro-geometric conjecture that claims that for an algebraic surface with b1=0 and b2>1 there cannot be b2 smooth disjoint complex curves of genus g>0 spanning the (rational) homology.