论文标题
可压缩空间和$ \ Mathcal {e} \ Mathcal {z} $ - 结构
Compressible Spaces and $\mathcal{E}\mathcal{Z}$-Structures
论文作者
论文摘要
BestVina引入了$ \ Mathcal {z} $ - 组$ g $的结构，以概括猫（0）或双曲线组的边界。 Farrell和Lafont引入的此概念的完善包括$ G $ - 均衡要求，被称为$ \ MATHCAL {E} \ MATHCAL {Z} $ - 结构。在本文中，我们表明，非主体弯曲的Riemannian $ n $ -n $ -manifolds的基本图群，接纳$ \ Mathcal {z} $ - 结构和图形和扁平弯曲或flat $ n $ -n $ -manifolds的图形，允许$ \ nathcal $ \ nathcal $ \ nathcal {e} {e} \ nathcal {z z} $ structures。这概括了前两位作者的最新结果，其中将$ \ Mathcal {e} \ Mathcal {z} $ - Baumslag-SoLitar群体上的结构和$ \ Mathcal {Z} $ - 在广义Baumslag-Solitar组上的结构。
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.
