关于流形的同胚群及其泛覆盖
On the homeomorphism groups of manifolds and their universal coverings
摘要：
令$\mathcal H_c(M)$表示流形$M$的所有紧支撑同胚的群的路连通单位连通区。证明了在对$M$的适当假设下，$\mathcal H_c(M)$是完美的和简单的.其次，考虑了$\H_c(M)$上的共轭不变范数，并研究了$\mathcal H_c(M)$的有界性.最后研究了$\mathcal H_c(M)$的泛覆叠群的结构。
英文摘要：
Let $\mathcal H_c(M)$ stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold $M$. It is shown that $\mathcal H_c(M)$ is perfect and simple under mild assumptions on $M$. Next, conjugation-invariant norms on $\H_c(M)$ are considered and the boundedness of $\mathcal H_c(M)$ is investigated. Finally, the structure of the universal covering group of $\mathcal H_c(M)$ is studied.
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。
