Subgroup chain generated by different shears in Aut(C^n)
科研大讨论系列报告
报告题目(Title)：Subgroup chain generated by different shears in Aut(C^n)
报告人(Speaker)：林章立博士 （北京雁栖湖应用数学研究院）
地点(Place)：教八114
时间(Time)：2023年9月22日，下午13:30-14:30
邀请人(Inviter)：汪志威
报告摘要
Fix an integer n> 2 and let $Aut(C^n)$ be the group of holomorphic automorphisms of $C^n$. We called $F\in Aut(C^n)$ a k-shear if F has simple form as $F(z)=(z_1,.…,z_{j-1},z_je^f+g, z_j+1,..,z_n)$, where $f, g \in O(C^k)$ are two functions in k variables among $z_1,..,\hat{z}_j,..., z_n$. Let $S^k$ be the subgroup generated by all k-shears, Apparently we have a subgroup chain $S^1 \subset.…. \subsect S^{n-1} \subset Aut(Cn)$. The famous Andersén-Lempert Theorm state that %S^{n-1} \noset Aut(Cn)$ but $S_1$ is dense in $Aut(C^n)$. So it is reasonable to ask whether the above subgroups are all distinct (by F. Forstneric). In this talk we show the answer is YES! We also consider similar problems on the volume-preserving subgroup $Aut_1(C^n)$ and symplectic subgroup $Aut_{sp}(C^{2n})$. This is a joint work with Xiangyu Zhou.
