曲面群扩张为CAT(0)群的单值性条件
Conditions on the monodromy for a surface group extension to be CAT(0)
AI总结：
该研究将Llosa Isenrich和Py关于曲面-曲面群为CAT(0)群的单值性必要条件推广到更一般情形，证明含正规曲面子群且商群满足特定性质的CAT(0)群的无限单值性表示核有限，且柱形双曲群满足该性质。
摘要：
为确定曲面-曲面丛何时是非正曲率的，Llosa Isenrich和Py给出了一个必要条件：给定具有无限单值性的曲面-曲面群$G$，若$G$是CAT(0)群，则单值性表示是单射的。我们将其推广为更一般的结论：设$G$是含正规曲面子群$R$的群。假设$G/R$满足如下性质：对$G/R$的每个无限正规子群$Λ$，存在无限子群$Λ_0<Λ$，使得中心化子$C_{G/R}(Λ_0)$是有限的。若$G$是具有无限单值性的CAT(0)群，则单值性表示的核是有限的。我们证明了柱形双曲群满足该性质。
英文摘要：
In order to determine when surface-by-surface bundles are non-positively curved, Llosa Isenrich and Py give a necessary condition: given a surface-by-surface group $G$ with infinite monodromy, if $G$ is CAT(0) then the monodromy representation is injective. We extend this to a more general result: Let $G$ be a group with a normal surface subgroup $R$. Assume $G/R$ satisfies the property that for every infinite normal subgroup $Λ$ of $G/R$, there is an infinite subgroup $Λ_0<Λ$ so that the centralizer $C_{G/R}(Λ_0)$ is finite. If $G$ is CAT(0) with infinite monodromy, then the monodromy representation has a finite kernel. We prove that acylindrically hyperbolic groups satisfy this property.
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。
