Boundary classification and two‐ended splittings of groups with isolated flats
Boundary classification and two‐ended splittings of groups with isolated flats
复制标题
孤立平面群的边界分类和两端分裂
作者：
M. Haulmark
本文给出了具有孤立平面群的一维边界的一个分类定理。给定一个群Γ几何上作用于具有孤立平面和一维边界的CAT(0)空间X，我们证明如果Γ不分裂在虚循环子群上，则∂X与圆、Sierpinski地毯或门格尔曲线同纯。这个定理推广了kapoich - kleiner的一个定理，解决了Kim Ruane的一个问题。
In this paper we provide a classification theorem for one‐dimensional boundaries of groups with isolated flats. Given a group Γ acting geometrically on a CAT(0) space X with isolated flats and one‐dimensional boundary, we show that if Γ does not split over a virtually cyclic subgroup, then ∂X is homeomorphic to a circle, a Sierpinski carpet, or a Menger curve. This theorem generalizes a theorem of Kapovich–Kleiner, and resolves a question due to Kim Ruane.