可压缩空间与$\mathcal{E}\mathcal{Z}$ -结构
Compressible Spaces and $\mathcal{E}\mathcal{Z}$-Structures
摘要：
Besthold为一个群$G$引入了一个$\mathcal{Z}$ -结构来推广CAT（0）或双曲群的边界。由Farrell和Lafont引入的这个概念的改进包括$G$ -等方差要求，并且被称为$\mathcal{E}\mathcal{Z}$ -结构。本文证明了非正曲的黎曼$n$ -流形的图的基本群具有$\mathcal{Z}$ -结构，而负曲的或平坦的$n$ -流形的图的基本群具有$\mathcal{E}\mathcal{Z}$ -结构.这推广了前两个作者与Tirel的最近结果，即把$\mathcal{E}\mathcal{Z}$ -结构放在Baumslag-Solitar群上，把$\mathcal{Z}$ -结构放在广义Baumslag-Solitar群上。
英文摘要：
Bestvina introduced a $\mathcal{Z}$-structure for a group $G$ to generalize the boundary of a CAT(0) or hyperbolic group. A refinement of this notion, introduced by Farrell and Lafont, includes a $G$-equivariance requirement, and is known as an $\mathcal{E}\mathcal{Z}$-structure. In this paper, we show that fundamental groups of graphs of nonpositively curved Riemannian $n$-manifolds admit $\mathcal{Z}$-structures and graphs of negatively curved or flat $n$-manifolds admit $\mathcal{E}\mathcal{Z}$-structures. This generalizes a recent result of the first two authors with Tirel, which put $\mathcal{E}\mathcal{Z}$-structures on Baumslag-Solitar groups and $\mathcal{Z}$-structures on generalized Baumslag-Solitar groups.
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