Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Agustin Moreno,海德堡大学
Inviter:	周正一
Title:	Symplectic structures from almost symplectic structures
Language:	English
Time & Venue:	2024.03.27 10:00-11:00 南楼N802
Abstract:	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.