CaltechAUTHORS
  A Caltech Library Service

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. https://resolver.caltech.edu/CaltechAUTHORS:20210112-105611010

[img] PDF - Published Version
See Usage Policy.

453Kb
[img] PDF - Accepted Version
See Usage Policy.

485Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20210112-105611010

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 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
Related URLs:
URLURL TypeDescription
https://doi.org/10.2140/agt.2020.20.3047DOIArticle
https://arxiv.org/abs/1807.10171arXivDiscussion Paper
ORCID:
AuthorORCID
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
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210112-105611010
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107422
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Jan 2021 19:06
Last Modified:12 Jan 2021 19:06

Repository Staff Only: item control page