Topological complexity of $S^3/Q_8$ as fibrewise L-S category - Iwase, Norio; Miyata, Yuya (Topological Methods in Nonlinear Analysis, 2023)
In 2010, M. Sakai and the first author showed that the topological complexityof a space $X$ coincides with the fibrewise unpointed L-S category of a pointed fibrewise space $\proj_{1} \colon X × X → X$ with the diagonal map$Δ \colon X → X × X$ 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.