Negative Sasakian structures on simply-connected 5-manifolds

2020/07/16 by Muñoz, V., Schütt, M., Tralle, A.
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2007.08597

Abstract

We study several questions on the existence of negative Sasakian structures on simply connected rational homology spheres and on Smale-Barden manifolds of the form #_k(S²× S³). First, we prove that any simply connected rational homology sphere admitting positive Sasakian structures also admits a negative one. This result answers the question, posed by Boyer and Galicki in their book [BG], of determining which simply connected rational homology spheres admit both negative and positive Sasakian structures. Second, we prove that the connected sum #_k(S²× S³) admits negative quasi-regular Sasakian structures for any k. This yields a complete answer to another question posed in [BG].

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