末态准三次集上的位形空间和有向路
Configuration spaces and directed paths on the final precubical set
摘要：
本文的主要目的是证明最终预三次集上的有向环空间同伦等价于平面上的点的“全”构形空间;“全”是指在一个构形中允许任何有限数目的点。我们还提供了几个应用：我们定义了新的预三次集的不变量，证明了任何预三次复形上的有向道路空间具有CW-复形的同伦类型，并构造了作为范畴神经的平面上的点的位形空间的某些表示。
英文摘要：
The main goal of this paper is to prove that the space of directed loops on the final precubical set is homotopy equivalent to the "total" configuration space of points on the plane; by "total" we mean that any finite number of points in a configuration is allowed. We also provide several applications: we define new invariants of precubical sets, prove that directed path spaces on any precubical complex have the homotopy types of CW-complexes and construct certain presentations of configuration spaces of points on the plane as nerves of categories.
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。
