Topological complexity of Khalimsky circles

2023/02/13 by Ryusei Yoshise, Yoshise, Ryusei
Computer Science · Mathematics · #06A07 #54H30 #55M30 #55P10 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2302.06380

openalex publication_date 2023/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We determine topological complexity of a series of finite spaces which is weakly homotopy equivalent to a circle S¹, and give a finite space X satisfying the inequality tc(X) < cat(X × X). This answers two conjectures on topological complexity for finite spaces raised by K. Tanaka in 2018.

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