Donaldson Question: “Tamed to Compatible”

：王宏玉（扬州大学）
：2023-07-08 16:00
：海韵园实验楼105报告厅

报告人：王宏玉（扬州大学）

时  间：2023年7月8日16:00

地  点：海韵园实验楼105报告厅

内容摘要:

In this talk, we show that on any tamed closed almost complex fourmanifold (M, J) whose dimension of J-anti-invariant cohomology is equal to self-dual second Betti number minus one, there exists a new symplectic form compatible with the given almost complex structure J. In particular, if the self-dual second Betti number is one, we give an affirmative answer to Donaldson question 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. Thus, our main result gives an affirmative answer to the Kodaira conjecture in symplectic version.

个人简介：

王宏玉，扬州大学数学科学学院教授、博士生导师，曾在新加坡国立大学任职，并任南京大学客座教授。主要研究微分几何, 偏微分方程及低维拓扑；近年来, 主要研究度量几何, 辛几何和非线性发展方程；在J. Diff. Geom., Peking Math. J., J. Geom. Anal.等学术期刊发表论文30余篇。

 

联系人：宋翀