Volume 20, issue 6 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Section problems for configurations of points on the Riemann sphere

Lei Chen and Nick Salter

Algebraic & Geometric Topology 20 (2020) 3047–3082
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 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.

Keywords
spherical braid group, configuration space, section, canonical reduction system
Mathematical Subject Classification 2010
Primary: 20F36, 55S40
References
Publication
Received: 6 June 2019
Revised: 26 October 2019
Accepted: 24 November 2019
Published: 8 December 2020
Authors
Lei Chen
Department of Mathematics
Caltech
Pasadena, CA
United States
Nick Salter
Department of Mathematics
Columbia University
New York, NY
United States