圆上映射类群作用的虚临界正则性
Virtual critical regularity of mapping class group actions on the circle
摘要：
我们证明了如果$G_1$和$G_2$是不可解群，则没有$(G_1\times G_2)*\mathbb{Z}$对$S^1$的$C^{1,τ}$作用忠实于$τ>0$ .作为推论，如果$S$是复杂度至少为3的可定向曲面，则映射类群$\mathrm{Mod}(S)$的任意有限指数子群关于圆的临界正则性至多为1，从而加强了前两位作者用Baik的一个结果.
英文摘要：
We show that if $G_1$ and $G_2$ are non-solvable groups, then no $C^{1,τ}$ action of $(G_1\times G_2)*\mathbb{Z}$ on $S^1$ is faithful for $τ>0$. As a corollary, if $S$ is an orientable surface of complexity at least three then the critical regularity of an arbitrary finite index subgroup of the mapping class group $\mathrm{Mod}(S)$ with respect to the circle is at most one, thus strengthening a result of the first two authors with Baik.
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。
