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Section problems for configurations of points on the Riemann sphere

Chen, Lei and Salter, Nick (2020) Section problems for configurations of points on the Riemann sphere. Algebraic & Geometric Topology, 20 (6). pp. 3047-3082. ISSN 1472-2739. doi:10.2140/agt.2020.20.3047.

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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 n ≠ 5, for which m can one continuously add m points to a configuration of n points? For n ≥ 6, we find that m must be divisible by n(n−1)(n−2), 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.

Item Type:Article
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URLURL TypeDescription Paper
Chen, Lei0000-0002-5941-7914
Additional Information:© 2020 Mathematical Sciences Publishers. Received: 6 June 2019; Revised: 26 October 2019; Accepted: 24 November 2019; Published: 8 December 2020.
Subject Keywords:spherical braid group, configuration space, section, canonical reduction system
Issue or Number:6
Classification Code:MSC 2010: Primary: 20F36, 55S40
Record Number:CaltechAUTHORS:20210112-105611010
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107422
Deposited By: Tony Diaz
Deposited On:12 Jan 2021 19:06
Last Modified:16 Nov 2021 19:02

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