圆上群作用的基本分拆与组合：Kathryn Mann定理的一种新方法
Basic partitions and combinations of group actions on the circle: A new approach to a theorem of Kathryn Mann
摘要：
设$Π_g$是亏格$g$（$g\geq2$）的曲面群，用$\RR_{Π_g}$表示从$Π_g$到$S^1$的保向同胚群的同态空间.设$2g-2=kl$对某些正整数$k$和$l$ .然后证明了由与某些同态的$k$ -折叠提升共轭且具有欧拉数$eu(φ)=l$的$φ$构成的$\RR_{Π_g}$的子集是闭集.这导致一个新的证明的主要结果凯瑟琳曼\cite{Mann}从一个完全不同的方法。
英文摘要：
Let $Π_g$ be the surface group of genus $g$ ($g\geq2$), and denote by $\RR_{Π_g}$ the space of the homomorphisms from $Π_g$ into the group of the orientation preserving homeomorphisms of $S^1$. Let $2g-2=kl$ for some positive integers $k$ and $l$. Then the subset of $\RR_{Π_g}$ formed by those $φ$ which are semiconjugate to $k$-fold lifts of some homomorphisms and which have Euler number $eu(φ)=l$ is shown to be clopen. This leads to a new proof of the main result of Kathryn Mann \cite{Mann} from a completely different approach.
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。
