Configurations and parallelograms associated to centers of mass
| dc.creator | Cohen, F R | |
| dc.creator | Kamiyama, Yasuhiko | |
| dc.date | 2009-03-27 | |
| dc.date.accessioned | 2026-07-07T12:57:33Z | |
| dc.date.available | 2026-07-07T12:57:33Z | |
| dc.description | The purpose of this article is to 1. define M(t,k) the t-fold center of mass arrangement for k points in the plane, 2. give elementary properties of M(t,k) and 3. give consequences concerning the space M(2,k) of k distinct points in the plane, no four of which are the vertices of a parallelogram. The main result proven in this article is that the classical unordered configuration of k points in the plane is not a retract up to homotopy of the space of k unordered distinct points in the plane, no four of which are the vertices of a parallelogram. The proof below is homotopy theoretic without an explicit computation of the homology of these spaces. In addition, a second, speculative part of this article arises from the failure of these methods in the case of odd primes p. This failure gives rise to a candidate for the localization at odd primes p of the double loop space of an odd sphere obtained from the p-fold center of mass arrangement. Potential consequences are listed. | |
| dc.description | This is the version published by Geometry & Topology Monographs on 14 November 2007 | |
| dc.identifier | https://arxiv.org/abs/0903.4867 | |
| dc.identifier | http://arxiv.org/abs/0903.4867 | |
| dc.identifier | Geom. Topol. Monogr. 11 (2007) 17-32 | |
| dc.identifier | doi:10.2140/gtm.2007.11.17 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224969 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 20F36, 55N25 | |
| dc.title | Configurations and parallelograms associated to centers of mass | |
| dc.type | text |