2000/02/10 by Raúl Ibáñez, Yuli Rudyak, Ibáñez, Raúl +6
Mathematics · #53C15 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG #msc:53C15
paper · pdf · doi:10.48550/arxiv.math/0002071
arxiv created 2000/02/10 · openalex publication_date 2000/02/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper deals with relations between the Hard Lefschetz property, (non)vanishing of Massey products and the evenness of odd-degree Betti numbers of closed symplectic manifolds. It is known that closed symplectic manifolds can violate all these properties (in contrast with the case of Kaehler manifolds). However, the relations between such homotopy properties seem to be not analyzed. This analysis may shed a new light on topology of symplectic manifolds. In the paper, we summarize our knowledge in tables (different in the simply-connected and in symplectically aspherical cases). Also, we discuss the variation of symplectically harmonic Betti numbers on some 6-dimensional manifolds.