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

By Tedi Drăghici, Tian-Jun Li, Weiyi Zhang. 2011

53 citations recorded by the source corpus.

For a compact almost complex 4-manifold $(M,J)$, we study the subgroups $H^{\pm}_J$ of $H^2(M, \mathbb{R})$ 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 $h^{\pm}_J$ are obtained for almost complex structures related to integrable ones. We also prove semi-continuity properties for $h^{\pm}_J$.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9aba2030d9b56c7543033da6c461253b2e54fdfd

How researchers see this paper

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In Applied Mathematics

1. Daniele Angella
2. Adriano Tomassini
3. J. Stelzig
4. Valentino Tosatti

In Geometry and Topology

1. Daniele Angella
2. Adriano Tomassini
3. J. Stelzig
4. Valentino Tosatti

Citations in the corpus

• On cohomological decomposition of almost-complex manifolds and deformations (2009, background): “This work has been originally developed as partial fulfillment for the first author’s Master Degreee in Matematica Pura e Applicata at Università di Parma under the supervision of the second author.”