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2019 Topological complexity of unordered configuration spaces of surfaces
Andrea Bianchi, David Recio-Mitter
Algebr. Geom. Topol. 19(3): 1359-1384 (2019). DOI: 10.2140/agt.2019.19.1359

Abstract

We determine the topological complexity of unordered configuration spaces on almost all punctured surfaces (both orientable and nonorientable). We also give improved bounds for the topological complexity of unordered configuration spaces on all aspherical closed surfaces, reducing it to three possible values. The main methods used in the proofs were developed in 2015 by Grant, Lupton and Oprea to give bounds for the topological complexity of aspherical spaces. As such this paper is also part of the current effort to study the topological complexity of aspherical spaces and it presents many further examples where these methods strongly improve upon the lower bounds given by zero-divisor cup-length.

Citation

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Andrea Bianchi. David Recio-Mitter. "Topological complexity of unordered configuration spaces of surfaces." Algebr. Geom. Topol. 19 (3) 1359 - 1384, 2019. https://doi.org/10.2140/agt.2019.19.1359

Information

Received: 23 February 2018; Revised: 21 October 2018; Accepted: 1 November 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07078607
MathSciNet: MR3954285
Digital Object Identifier: 10.2140/agt.2019.19.1359

Subjects:
Primary: 55M99, 55P20
Secondary: 20J06, 55M30, 68T40

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 3 • 2019
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