On tamed almost complex four manifolds
Differential Geometry
2019-11-27 v3
Abstract
This paper proves that on any tamed closed almost complex four-manifold whose dimension of -anti-invariant cohomology is equal to the self-dual second Betti number minus one, there exists a new symplectic form compatible with the given almost complex structure . In particular, if the self-dual second Betti number is one, we give an affirmative answer to a question of Donaldson for tamed closed almost complex four-manifolds. Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira conjecture.
Cite
@article{arxiv.1712.02948,
title = {On tamed almost complex four manifolds},
author = {Qiang Tan and Hongyu Wang and Jiuru Zhou and Peng Zhu},
journal= {arXiv preprint arXiv:1712.02948},
year = {2019}
}