论文标题
跨性摩尔斯边界II：适当的测量空间
Sublinearly Morse Boundary II: Proper geodesic spaces
论文作者
论文摘要
我们为任何适当的测量指标空间建立了Gromov边界的类似物，因此对于任何有限生成的组。更确切地说，对于任何适当的测量公制空间$ x $和任何sublinear函数$κ$，我们为$ x $构建一个边界，表示$ \ mathcal {\ partial}_κx $，即quasi-is-Ismets上是不变的且可转移的。作为一个应用程序，我们表明，当$ g $是有限类型表面的映射类组或相对双曲线的组时，然后使用最小的假设，$ g $的泊松边界可以在$κ$ g $的$ g $边界上实现，配备了与任何有限生成集相关的单词度量。
We build an analogue of the Gromov boundary for any proper geodesic metric space, hence for any finitely generated group. More precisely, for any proper geodesic metric space $X$ and any sublinear function $κ$, we construct a boundary for $X$, denoted $\mathcal{\partial}_κ X$, that is quasi-isometrically invariant and metrizable. As an application, we show that when $G$ is the mapping class group of a finite type surface, or a relatively hyperbolic group, then with minimal assumptions the Poisson boundary of $G$ can be realized on the $κ$-Morse boundary of $G$ equipped the word metric associated to any finite generating set.
