Geodesic
Section problems for configurations of points on the Riemann sphere
Chen, Lei1 ; Salter, Nick2
1Department of Mathematics, Caltech, Pasadena, CA, United States
2Department of Mathematics, Columbia University, New York, NY, United States
Algebraic and Geometric Topology, Tome 20 (2020) no. 6, pp. 3047-3082
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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.

Classification : 20F36, 55S40
Keywords: spherical braid group, configuration space, section, canonical reduction system

Chen, Lei  1   ; Salter, Nick  2

1 Department of Mathematics, Caltech, Pasadena, CA, United States
2 Department of Mathematics, Columbia University, New York, NY, United States 
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Chen, Lei; Salter, Nick. Section problems for configurations of points on the Riemann sphere. Algebraic and Geometric Topology, Tome 20 (2020) no. 6, pp. 3047-3082. http://geodesic.mathdoc.fr/item/AGT_2020_20_6_a8/

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