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Adding a point to configurations in closed balls

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.

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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
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URLURL TypeDescription Paper
Chen, Lei0000-0002-5941-7914
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.
Funding AgencyGrant Number
Issue or Number:2
Classification Code:MSC (2010): Primary 55M20, 55R80; Secondary 20F36
Record Number:CaltechAUTHORS:20200319-085439482
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101990
Deposited By: Tony Diaz
Deposited On:19 Mar 2020 16:10
Last Modified:16 Nov 2021 18:07

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