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A combinatorial description of topological complexity for finite spaces

Kohei Tanaka

Algebraic & Geometric Topology 18 (2018) 779–796
Abstract

This paper presents a discrete analog of topological complexity for finite spaces using purely combinatorial terms. We demonstrate that this coincides with the genuine topological complexity of the original finite space. Furthermore, we study the relationship with simplicial complexity for simplicial complexes by taking the barycentric subdivision into account.

Keywords
topological complexity, finite space, order complex
Mathematical Subject Classification 2010
Primary: 55P10
Secondary: 06A07
References
Publication
Received: 25 May 2016
Revised: 1 October 2017
Accepted: 15 October 2017
Published: 12 March 2018
Authors
Kohei Tanaka
Institute of Social Sciences, School of Humanities and Social Sciences
Academic Assembly
Shinshu University
Matsumoto
Japan