与质心相关的平行四边形
Configurations and parallelograms associated to centers of mass
摘要：
这篇文章的目的是1。定义M（t，k）为平面中k个点的t重质心排列，2.给出了M（t，k）和3的基本性质。给出了关于平面上k个不同点的空间M（2，k）的结论，其中没有四个点是一个点的顶点。本文证明了平面上k点的经典无序构形不是平面上k个无序相异点空间的上至同伦的收缩，其中k个无序相异点空间中没有四个是顶点空间的顶点。下面的证明是同伦理论的，没有明确计算这些空间的同调。此外，第二，投机性的一部分，本文产生于这些方法的失败的情况下，奇素数p.这种失败引起了一个候选人的本地化在奇素数p的双闭路空间的奇球从p-折叠中心的质量安排。列出了潜在后果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
