Homotopic properties of Kähler orbifolds

2016/05/10 by Bazzoni, Giovanni, Biswas, Indranil, Fernández, Marisa +2
#55S30 #57R18 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1605.03024

Abstract

We prove the formality and the evenness of odd-degree Betti numbers for compact Kähler orbifolds, by adapting the classical proofs for Kähler manifolds. As a consequence, we obtain examples of symplectic orbifolds not admitting any Kähler orbifold structure. We also review the known examples of non-formal simply connected Sasakian manifolds, and produce an example of a non-formal quasi-regular Sasakian manifold with Betti numbers b₁=0 and b₂ > 1.

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