论文标题
同型非紧密连接的CW复合物的收缩楔形组
Homotopy groups of shrinking wedges of non-simply connected CW-complexes
论文作者
论文摘要
在本文中，我们研究了一个序列$ \ {x_j \} $的nink楔$ x $的同型组，该序列是非微连接的cw-complexes。使用广义覆盖空间理论和形状理论的结合，我们构建了一个规范的同构$θ：π_n（x）\ to \ prod_ {j \ in \ mathbb {n}} \ bigoplus_ {π_1（x）/π_1（x_j）} $ imigize $ i.每次通用封面$ \ widetilde {x} _j $是$（n-1）$ - 连接时，注射剂。这些结果（1）提供了$ n $ th同置$ \ Mathbb {rp}^n $ nink wedge的特征，（2）提供了$π_2$的$π_2$的特征，（（3）暗示着Auspherical cw-complexes is aspherical is aspherical is aspherical is aspherical is a spherical is aspherical is aspherical。
In this paper, we study the homotopy groups of a shrinking wedge $X$ of a sequence $\{X_j\}$ of non-simply connected CW-complexes. Using a combination of generalized covering space theory and shape theory, we construct a canonical homomorphism $$Θ:π_n(X)\to\prod_{j\in\mathbb{N}}\bigoplus_{π_1(X)/π_1(X_j)}π_n(X_j),$$ characterize its image, and prove that $Θ$ is injective whenever each universal cover $\widetilde{X}_j$ is $(n-1)$-connected. These results (1) provide a characterization of the $n$-th homotopy group of the shrinking wedge of copies of $\mathbb{RP}^n$, (2) provide a characterization of $π_2$ of an arbitrary shrinking wedge, and (3) imply that a shrinking wedge of aspherical CW-complexes is aspherical.
