报告题目：Every $S^2$-Bundle over a closed Surface has infinite Mapping Class Group

报告人：郭慧正 博士后 中国科学技术大学

报告时间：2026.11.10 9:00-10:00

报告地点：#腾讯会议：559-911-464

校内联系人：王骁 [email protected]

报告摘要：In 2025, Lin, Wu, Xie and Zhang extend Dax invariant from embedded disks to embedded surfaces and show that there is surjective homomorphism from $MCG(M)$ to $\mathbb{Z}^{\infty}$ for $M= \Sigma \times S^2$. Let $\Sigma$ be a closed surface, in the paper we show that for any nontrivial $S^2$ fiber bundles $X= \Sigma \ltimes S^2$, whether orientable or nonorientable, there is surjective homomorphisms from $MCG(X)$ to $\mathbb{Z}^{\infty}$. The proof is an application of generalization of Dax invariants for embedded surfaces. The property of $MCG(X)$ inherits from trivial fiber bundle $\Sigma \times S^2$ and main theorem shows that the algebraic size of the smooth mapping class group of $S^2$-fiber bundles does not depend on the triviality of the bundle. In the talk, we also go through the construction of barbell diffeomorphism and Dax invariant.

报告人简介：

郭慧正，中国科学技术大学国际几何与物理中心（IGP）博士后研究员，博士毕业于美国乔治·华盛顿大学，师从Józef H. Przytycki教授。主要研究兴趣为低维拓扑，尤其是纽结理论、三维与四维流形、映射类群及量子拓扑不变量。研究涉及Alexander不变量、Khovanov同调、Kauffman bracket skein module、cubic skein module等。研究成果发表于《Algebraic & Geometric Topology》《Homology, Homotopy and Applications》等国际数学期刊。