A combinatorial description of topological complexity for finite spaces

Tanaka, Kohei

doi:10.2140/agt.2018.18.779

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A combinatorial description of topological complexity for finite spaces

Kohei Tanaka

Algebraic & Geometric Topology 18 (2018) 779–796

DOI: 10.2140/agt.2018.18.779

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

Volume 18, issue 2 (2018)