On the J-anti-invariant cohomology of almost complex 4-manifolds
Tedi Draghici, Tian-Jun Li, Weiyi Zhang

TL;DR
This paper investigates the structure of certain cohomology subgroups in almost complex 4-manifolds, revealing generic triviality of the anti-invariant subgroup and establishing semi-continuity properties of their dimensions.
Contribution
It provides new results on the behavior of J-anti-invariant cohomology classes, including generic triviality and semi-continuity, for almost complex 4-manifolds.
Findings
H^-_J subgroup is trivial for generic structures when b^+ = 1
Computed dimensions h^{ ext{±}}_J for related structures
Established semi-continuity properties for h^{ ext{±}}_J
Abstract
For a compact almost complex 4-manifold , we study the subgroups of consisting of cohomology classes representable by -invariant, respectively, -anti-invariant 2-forms. If , we show that for generic almost complex structures on , the subgroup is trivial. Computations of the subgroups and their dimensions are obtained for almost complex structures related to integrable ones. We also prove semi-continuity properties for .
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Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows
