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arXiv · 2302.06380

Topological complexity of Khalimsky circles

Ryusei Yoshise
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Abstract

We determine topological complexity of a series of finite spaces which is weakly homotopy equivalent to a circle $S^1$, and give a finite space $X$ satisfying the inequality tc$(X) <$ cat$(X {\times} X)$. This answers two conjectures on topological complexity for finite spaces raised by K. Tanaka in 2018.

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Ryusei Yoshise. 2023-02-13. Topological complexity of Khalimsky circles. https://arxiv.org/abs/2302.06380

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