论文标题
狭窄的空间
Weakly Chained Spaces
论文作者
论文摘要
我们介绍了“弱连锁空间”，这些空间无需局部连接或连接，但对此有一个合理的概念，即广义基本组和相关的广义通用覆盖。我们表明，在紧凑的度量案例中，弱链条等同于经典形状理论中“尖头可移动”的概念。我们使用这个事实和Geoghegan-Swenson的定理来给出猫（0）空间中的度量球的标准，这意味着边界在无穷大的基本组中具有可分离的基本组。
We introduce "weakly chained spaces", which need not be locally connected or path connected, but for which one has a reasonable notion of generalized fundamental group and associated generalized universal cover. We show that in the compact metric case, weakly chained is equivalent to the concept of "pointed 1-movable" from classical shape theory. We use this fact and a theorem of Geoghegan-Swenson to give criteria on the metric spheres in a CAT(0) space that imply that the boundary is has semistable fundamental group at infinity.
