arXiv subjects

Yuya Miyata

Publications and source records attributed to Yuya Miyata.

2 recordsLinked to original sources

arXiv2023

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 $\operatorname{pr}_{1} : X \times X \to X$ with the diagonal map $Δ: X \to X \times X$ 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.

math.AT↗

arXiv2019

On the topological complexity of $S^3/Q_8$

Topological complexity was first introduced in 2003 by Michael Farber as a homotopy invariant for a connected topological space X, denoted by TC(X). Although the invariant is defined in terms of elementary homotopy theory using well-known Serre path fibration, not many examples are known to be determined concretely by now. In 2010, Iwase and Sakai showed that the topological complexity of a space is a fibrewise version of a L-S category for a fibrewise space over the space. In this paper, we determine the topological complexity of $S^3/Q_8$ using a method produced from the fibrewise view point.

math.AT↗