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

Qiang Tan; Hongyu Wang; Jiuru Zhou

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

Symplectic Geometry 2016-11-15 v3

Authors: Qiang Tan , Hongyu Wang , Jiuru Zhou

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.

Keywords

almost contact manifolds smooth 4-manifolds kähler manifolds

Cite

@article{arxiv.1411.4103,
  title  = {A note on the deformations of almost complex structures on compact four-manifolds},
  author = {Qiang Tan and Hongyu Wang and Jiuru Zhou},
  journal= {arXiv preprint arXiv:1411.4103},
  year   = {2016}
}