2013/12/27 by Mizuki Furuse, Furuse, Mizuki, Takashi Mukouyama +3 · 1 citation
Computer Science · Mathematics · #55R80 #57N80 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #msc:55R80 #msc:57N80
paper · pdf · doi:10.48550/arxiv.1312.7368
44 pages. v2. Typos fixed. Accepted for publication by Topological Methods in Nonlinear Analysis
openalex publication_date 2013/12/27 · arxiv created 2014/07/17 · arxiv updated 2014/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of regular cell complexes plays a central role in topological combinatorics because of its close relationship with posets. A generalization, called totally normal cellular stratified spaces, was introduced by the third author by relaxing two conditions; face posets are replaced by acyclic categories and cells with incomplete boundaries are allowed. The aim of this article is to demonstrate the usefulness of totally normal cellular stratified spaces by constructing a combinatorial model for the configuration space of graphs. As an application, we obtain a simpler proof of Ghrist's theorem on the homotopy dimension of the configuration space of graphs. We also make sample calculations of the fundamental group of ordered and unordered configuration spaces of two points for small graphs.