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arXiv · 2208.07117

Topological Complexity of $S^3/Q_8$ as fibrewise L-S category

Norio Iwase·Yuya Miyata
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Abstract

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 $\operatorname{pr}_{1} : X \times X \to X$ with the diagonal map $\Delta : X \to X \times X$ 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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Norio Iwase, Yuya Miyata. 2022-08-15. Topological Complexity of $S^3/Q_8$ as fibrewise L-S category. https://doi.org/10.12775/tmna.2022.068

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