A note on the deformations of almost complex structures on compact four-manifolds

Abstract

In this paper, we calculate the dimension of the $J$-anti-invariant cohomology subgroup $H_J^{-}$ on ${\mathbb{T}}^4$. Inspired by the concrete example, ${\mathbb{T}}^4$, we get that: On a closed symplectic $4$-dimensional manifold $(M,\omega )$, $h_J^{-}=0$ for generic $\omega$-compatible almost complex structures.

arXiv admin note: text overlap with arXiv:1112.0768

References in corpus (2)

• On nodal sets for Dirac and Laplace operators
• Primitive cohomology of degree 2 on compact symplectic manifolds