中科院数学与系统科学研究院

数学研究所

学术报告

拓扑研讨班

报告人：Agustin Moreno（海德堡大学）

题  目：Symplectic structures from almost symplectic structures

时  间：2024.03.27（星期三）10:00-11:00

地  点：数学院南楼N802

摘  要：In this talk, we will consider a stabilized version of the fundamental existence problem of symplectic structures. Given a formal symplectic manifold, i.e. a closed manifold M with a non-degenerate 2-form and a non-degenerate second cohomology class, we investigate when its natural stabilization to M x T^2 can be realized by a symplectic form. We show that this can be done whenever the formal symplectic manifold admits a symplectic divisor. It follows that the product with T^2 of an almost symplectic blow up admits a symplectic form. Another corollary is that if a formal symplectic 4-manifold, which either satisfies that its positive/negative second betti numbers are both at least 2, or that is simply connected, then Mx T^2 is symplectic. 

This is joint work with Fabio Gironella, Fran Presas, Lauran Touissant.