Mathematics – Algebraic Topology
Scientific paper
2009-03-27
Geom. Topol. Monogr. 11 (2007) 17-32
Mathematics
Algebraic Topology
This is the version published by Geometry & Topology Monographs on 14 November 2007
Scientific paper
10.2140/gtm.2007.11.17
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.
Cohen Frederick R.
Kamiyama Yasuhiko
No associations
LandOfFree
Configurations and parallelograms associated to centers of mass does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Configurations and parallelograms associated to centers of mass, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Configurations and parallelograms associated to centers of mass will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-21937