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Mathematics > Algebraic Topology
Title: Topological complexity of Khalimsky circles
(Submitted on 13 Feb 2023)
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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