论文标题
表面组扩展为CAT的单构型的条件（0）
Conditions on the monodromy for a surface group extension to be CAT(0)
论文作者
论文摘要
为了确定何时逐个表面捆绑包非阳性弯曲，llosa isenrich和py给出了必要的条件：给定一个逐表面的$ g $带有无限单型的$ g $，如果$ g $是cat（0），则单调性表示为注射。我们将其扩展到更一般的结果：让$ g $是一个具有普通表面亚组$ r $的组。假设$ g/r $满足每个无限的普通子组$ g/r $的属性，有一个无限的子组$λ_0<λ$，以便centralizer $ c_ {g/r}（λ_0）$是有限的。如果$ g $是带有无限单曲的CAT（0），则单片表示为有限的内核。我们证明，酰基柔性基团满足了这一特性。
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.
