配置空间与最终预割集上的有向路径

IF 0.5 3区 数学 Q3 MATHEMATICS
Jakub Paliga, Krzysztof Ziemia'nski
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引用次数: 1

摘要

本文的主要目的是证明最终立方集上的有向环空间与平面上点的“全”位形空间是同伦等价的;我们所说的“总数”是指在一个构型中允许有有限数量的点。我们还给出了几个应用:我们定义了新的预立方集不变量,证明了任意预立方复上的有向路径空间具有cw -复的同伦类型,构造了平面上点的位形空间作为范畴神经的某些表示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Configuration spaces and directed paths on the final precubical set
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.
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来源期刊
Fundamenta Mathematicae
Fundamenta Mathematicae 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
44
审稿时长
6-12 weeks
期刊介绍: FUNDAMENTA MATHEMATICAE concentrates on papers devoted to Set Theory, Mathematical Logic and Foundations of Mathematics, Topology and its Interactions with Algebra, Dynamical Systems.
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