Chen, Lei and Gadish, Nir and Lanier, Justin (2020) Adding a point to configurations in closed balls. Proceedings of the American Mathematical Society, 148 (2). pp. 885-891. ISSN 0002-9939. doi:10.1090/proc/14712. https://resolver.caltech.edu/CaltechAUTHORS:20200319-085439482
![[img]](https://authors.library.caltech.edu/style/images/fileicons/application_pdf.png) |
PDF
- Submitted Version
See Usage Policy. 119kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20200319-085439482
Abstract
We answer the question of when a new point can be added in a continuous way to configurations of n distinct points in a closed ball of arbitrary dimension. We show that this is possible given an ordered configuration of n points if and only if n ≠ 1. On the other hand, when the points are not ordered and the dimension of the ball is at least 2, a point can be added continuously if and only if n = 2. These results generalize the Brouwer fixed-point theorem, which gives the negative answer when n = 1. We also show that when n = 2, there is a unique solution to both the ordered and unordered versions of the problem up to homotopy.
| Item Type: | Article | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Related URLs: |
| |||||||||
| ORCID: |
| |||||||||
| Alternate Title: | Generalizing Brouwer: adding points to configurations in closed balls | |||||||||
| Additional Information: | © 2019 American Mathematical Society. Received by editor(s): December 19, 2018; Received by editor(s) in revised form: May 6, 2019, and May 20, 2019. Published electronically: October 18, 2019. The third author was supported by the NSF grant DGE-1650044. Communicated by: David Futer. | |||||||||
| Funders: |
| |||||||||
| Issue or Number: | 2 | |||||||||
| Classification Code: | MSC (2010): Primary 55M20, 55R80; Secondary 20F36 | |||||||||
| DOI: | 10.1090/proc/14712 | |||||||||
| Record Number: | CaltechAUTHORS:20200319-085439482 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200319-085439482 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 101990 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 19 Mar 2020 16:10 | |||||||||
| Last Modified: | 16 Nov 2021 18:07 |
Repository Staff Only: item control page
