$S^3/Q_8$的拓扑复杂度作为光纤的L-S范畴

Pub Date : 2023-09-23 DOI:10.12775/tmna.2022.068
Norio Iwase, Yuya Miyata
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引用次数: 0

摘要

2010年,M. Sakai和第一作者证明了空间$X$的拓扑复杂度与指向的纤维空间$\proj_{1} \冒号X \乘以X$的沿纤维无点L-S范畴重合,其对角线映射$\Delta \冒号X \到X \乘以X$为其截面。在本文中,我们描述了如何确定一个拓扑球面空间形式的纤维L-S范畴或拓扑复杂度的算法。特别是,对于$S^3/Q_8$,其中$Q_8$为四元数组,我们编写了python代码来实现该算法,以确定其拓扑复杂度。
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Topological complexity of $S^3/Q_8$ as fibrewise L-S category
In 2010, M. Sakai and the first author showed that the topological complexity of a space $X$ coincides with the fibrewise unpointed L-S category of a pointed fibrewise space $\proj_{1} \colon X \times X \to X$ with the diagonal map $\Delta \colon X \to X \times X$ as its section. In this paper, we describe our algorithm how to determine the fibrewise L-S category or the Topological Complexity of a topological spherical space form. Especially, for $S^3/Q_8$ where $Q_8$ is the quaternion group, we write a python code to realise the algorithm to determine its Topological Complexity.
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