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2018 Topological complexity of $n$ points on a tree
Steven Scheirer
Algebr. Geom. Topol. 18(2): 839-876 (2018). DOI: 10.2140/agt.2018.18.839

Abstract

The topological complexity of a path-connected space X , denoted by TC ( X ) , can be thought of as the minimum number of continuous rules needed to describe how to move from one point in X to another. The space X is often interpreted as a configuration space in some real-life context. Here, we consider the case where X is the space of configurations of n points on a tree Γ. We will be interested in two such configuration spaces. In the first, denoted by C n ( Γ ) , the points are distinguishable, while in the second, UC n ( Γ ) , the points are indistinguishable. We determine TC ( UC n ( Γ ) ) for any tree Γ and many values of n , and consequently determine TC ( C n ( Γ ) ) for the same values of n (provided the configuration spaces are path-connected).

Citation

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Steven Scheirer. "Topological complexity of $n$ points on a tree." Algebr. Geom. Topol. 18 (2) 839 - 876, 2018. https://doi.org/10.2140/agt.2018.18.839

Information

Received: 2 August 2016; Revised: 5 February 2017; Accepted: 4 April 2017; Published: 2018
First available in Project Euclid: 22 March 2018

zbMATH: 06859607
MathSciNet: MR3773741
Digital Object Identifier: 10.2140/agt.2018.18.839

Subjects:
Primary: 57M15
Secondary: 55R80, 57Q05

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 2 • 2018
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