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2020 Section problems for configurations of points on the Riemann sphere
Lei Chen, Nick Salter
Algebr. Geom. Topol. 20(6): 3047-3082 (2020). DOI: 10.2140/agt.2020.20.3047

Abstract

We prove a suite of results concerning the problem of adding m distinct new points to a configuration of n distinct points on the Riemann sphere, such that the new points depend continuously on the old. Altogether, these results provide a complete answer to the following question: given n5, for which m can one continuously add m points to a configuration of n points? For n6, we find that m must be divisible by n(n1)(n2), and we provide a construction based on the idea of cabling of braids. For n=3,4, we give some exceptional constructions based on the theory of elliptic curves.

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Lei Chen. Nick Salter. "Section problems for configurations of points on the Riemann sphere." Algebr. Geom. Topol. 20 (6) 3047 - 3082, 2020. https://doi.org/10.2140/agt.2020.20.3047

Information

Received: 6 June 2019; Revised: 26 October 2019; Accepted: 24 November 2019; Published: 2020
First available in Project Euclid: 16 December 2020

MathSciNet: MR4185935
Digital Object Identifier: 10.2140/agt.2020.20.3047

Subjects:
Primary: 20F36 , 55S40

Keywords: canonical reduction system , configuration space , section , spherical braid group

Rights: Copyright © 2020 Mathematical Sciences Publishers

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