Loops of diffeomorphisms and symplectomorphisms on 4-manifolds (四维流形光滑自同胚群与辛自同胚群中的闭路)
报告题目(Title)：Loops of diffeomorphisms and symplectomorphisms on 4-manifolds (四维流形光滑自同胚群与辛自同胚群中的闭路)
报告人(Speaker)：Jianfeng Lin（UCSD）
地点(Place)：线下: 后主楼1124 （线上ZoomID: 984 3673 2943 Password: 301959)
时间(Time)：2021.5.28 10:00am-11:00am
邀请人(Inviter)：张泽州
报告摘要
Let Symp(X) be the group of symplectomorphisms on a symplectic 4-manifold X. It is a classical problem in symplectic topology to study the homotopy type of Symp(X) and to compare it with the group of all diffeomorphisms on X. For a large class of symplectic manifolds, Seidel proved that the square of the Dehn twist along an embedded Lagrangian 2-sphere is smoothly isotopic to the identity map but not symplectically so. In this talk, we will recall related backgrounds and then discuss the following new result: For any X that contains a smoothly embedded 2-sphere with self-intersection -1 or -2, there exists a loop of self-diffeomorphisms on X that is not homotopic to a loop of symplectomorphisms. This result generalizes previous works of Kronheimer and Smirnov. And it is closely related to Seidel’s result. The key ingredient is a new gluing formula for the family Seiberg-Witten invariant.
