中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

拓扑研讨班

Speaker: 林剑锋 教授（清华大学）

Inviter: 苏阳

Language: Chinese

Title: Lightbulb theorem, embedded surfaces and isotopy of symplectic structures

Time & Venue: 2025年12月24日（星期三）14：30-15：30 & 南楼N820

Abstract: Gabai's lightbulb theorem  classifies embedded spheres in 4-manifolds with a geometric dual sphere. It is a breakthrough in 4-dimensional topology. In this talk, I discuss a joint work with Weiwei Wu, Yi Xie and Boyu Zhang, which classifies the isotopy classes of embeddings of a surface F into the product manifold F cross S2 with a geometric dual.  This answers a question of Gabai regarding the generalized lightbulb theorem. Second, we show that the space of symplectic forms on an irrational ruled surface in a fixed cohomology class has infinitely many connected components. This gives the first such example among closed 4--manifolds and answers Problem 2(a) in McDuff--Salamon's problem list.  The proofs are based on a generalization of the Dax invariant to embedded closed surfaces. In the proof, we also establish several properties of the smooth mapping class group of a surface cross S2 is infinitely generated.