手柄体组的刚性和柔性
Rigidity and Flexibility for Handlebody Groups
摘要：
证明了亏格$g$的有限指数子群到亏格$g$映射类群的任意内射映射都是由映射类群元素共轭的.另一方面，我们构造了亏格$g$映射体群到亏格$h>g$映射类群的一个注入，该映射群不共轭到一个映射体群。
英文摘要：
We show that finite index subgroups of the handlebody group are rigid in their ambient mapping class group: any injective map of a finite index subgroup of the genus $g$ handlebody group into the genus $g$ mapping class group is conjugation by a mapping class group element. On the other hand, we construct an injection of the genus $g$ handlebody group into a genus $h>g$ mapping class group which is not conjugate into a handlebody group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
