中科院数学与系统科学研究院
数学研究所
拓扑研讨班
报告人：林剑锋 教授（清华大学，丘成桐数学科学中心）
题 目：Nonexistence of symplectic structures on certain family of 4-manifolds
时 间：2021.12.08（星期三），14:30-15 :30
地 点：南楼N802室
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. This problem is closely related to the existence of symplectic structures on smooth families of 4-manifolds. In this talk, we will discuss the following new results: (1) 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. (2) Consider a family of 4-manifolds obtained by resolving an ADE singularity using a hyperkahler family of complex structures, this family never support a family symplectic structure in a constant cohomology class. (3) For any nonminimal symplectic 4-manifold whose positive second-betti number does not equal to 3, the space of symplectic form is not simply connected. The key ingredient in the proofs is a new gluing formula for the family Seiberg-Witten invariant.
附件：