论文标题
粗$ \ Mathcal {z} $ - 组的边界
Coarse $\mathcal{Z}$-Boundaries for Groups
论文作者
论文摘要
我们将BESTVINA的概念概括为$ \ MATHCAL {z} $ - 一个组的边界，即“粗$ \ Mathcal {Z} $ - 边界”的概念。我们表明，建立了关于$ \ MATHCAL {Z} $的定理 - 边界对更一般的理论很好地延续了，并且在$ \ Mathcal {Z} $的某些构想属性中，当适用于Roble $ \ Mathcal {Z} $ - 边界时，将变成定理。最值得注意的是，承认粗糙的$ \ MATHCAL {z} $ - 边界的属性是纯正的静电法不变。在此过程中，我们通过引入“模型$ \ Mathcal {z} $几何形状”的概念来简化新的定义和现有定义。根据现有的理论，我们还开发了上述的模棱两可的版本 - “粗$ e \ Mathcal {z} $ - 边界”。
We generalize Bestvina's notion of a $\mathcal{Z}$-boundary for a group to that of a "coarse $\mathcal{Z}$-boundary." We show that established theorems about $\mathcal{Z}$-boundaries carry over nicely to the more general theory, and that some wished-for properties of $\mathcal{Z}$-boundaries become theorems when applied to coarse $\mathcal{Z}$-boundaries. Most notably, the property of admitting a coarse $\mathcal{Z}$-boundary is a pure quasi-isometry invariant. In the process, we streamline both new and existing definitions by introducing the notion of a "model $\mathcal{Z}$-geometry." In accordance with the existing theory, we also develop an equivariant version of the above -- that of a "coarse $E\mathcal{Z}$-boundary."
