Abstract
We prove a suite of results concerning the problem of adding distinct new points to a configuration of 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 , for which can one continuously add points to a configuration of points? For , we find that must be divisible by , and we provide a construction based on the idea of cabling of braids. For , we give some exceptional constructions based on the theory of elliptic curves.
Citation
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
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