University Seminar-: Computability, Complexity, and Algebraic Structure-On the mapping class group of nontrivial S2 fiber bundles

Time: Wednesday, April 29, 5:00–6:00 pm

Place: Phillips Hall, Room 108

Speaker: Huizheng (Ali) Guo, GWU

Title: On the mapping class group of nontrivial S² fiber bundles

Abstract:  Mapping class groups play a central role in low-dimensional topology, encoding the symmetries of manifolds up to isotopy. In dimension four, however, much less is understood about their algebraic structure. In recent work of Lin, Wu, Xie and Zhang, they construct generalization of Dax invariants for closed embedding surfaces to show that the mapping class group of the trivial bundle $MCG(S^2\time \Sigma)$ surjects onto $\mathbb{Z}^{\infty}$. In this talk, we apply the generalization of Dax invariant and extend the proof to the nontrivial bundle $S^2 \ltimes \Sigma$. We show that there is also a surjective homomorphism from $MCG(S^2 \ltimes \Sigma)$ to $\mathbb{Z}^{\infty}$ whose restriction on $MCG_0(S^2 \ltimes \Sigma)$ also has the infinity surjectivity property. 

After the research talk, I will share information and experience on how to apply for postdoc positions (research oriented) globally, including but not limited to material preparation, job market information, timeline, interviews, and offer decisions.