On the J-anti-invariant cohomology of almost complex 4-manifolds

2011/04/13 by Draghici, Tedi, Li, Tian-Jun, Zhang, Weiyi · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1104.2511

Abstract

For a compact almost complex 4-manifold (M,J), we study the subgroups H^±_J of H²(M, ℝ) consisting of cohomology classes representable by J-invariant, respectively, J-anti-invariant 2-forms. If b⁺ =1, we show that for generic almost complex structures on M, the subgroup H^-_J is trivial. Computations of the subgroups and their dimensions h^±_J are obtained for almost complex structures related to integrable ones. We also prove semi-continuity properties for h^±_J.

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• Hodge decomposition and Hard Lefschetz Condition on almost Kähler manifolds

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