报告题目：Dolbeaut cohomology group 1,2,3,4,5

报告摘要：For compact complex surfaces, the existence of Kahler structure is a topological condition, i.e., $b_1$ is even. However, by the exotic phenomenon in smooth $4$ manifolds, the existence of symplectic structure can not be a topological obstruction for compact almost complex $4$ manifolds. In these talks, we define a refined Dolbeault cohomology on almost complex manifolds. We give a condition for a compact almost complex 4 manifold admitting a symplectic structure. Moreover, we prove that such a sufficient condition is equivalent to the ddbar-lemma, which is similar to the case of compact complex surfaces.This result can be viewed as symplectic proof to Kodaira's conjecture. Meanwhile, we show that on compact almost complex $4$ manifolds the Frolicher type equality on $b_1$ does not hold in general, only the Frolicher type inequality holds. This is quite different to the case of compact complex surfaces.

报 告 人：林德燮，重庆大学博士后助理研究员。2020年博士毕业于东京大学。研究方向是指标理论，规范场4 维近复流形。

报告时间：2024年1月22、24、26、28、30日（星期一、三、五、日、二）上午9:30-11:30

报告地点：数学科学学院306

主办单位：数学科学学院

联系人：王宏玉

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