2022/08/30 by Xinxing Tang, Shing–Tung Yau, Tang, Xinxing +1
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2208.14063
openalex publication_date 2022/08/30 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
In this paper, firstly, we will study the structure of the path complex (Ω_*(G;\Z),∂) of a digraph G via the \Z-generators of Ω_*(G,\Z) under strongly regular condition, which is called the minimal path in \citeHY. In particular, we will study various examples of the minimal 3-paths. Secondly, we will show that the supporting sub-digraph of minimal path has acyclic path homologies. Thirdly, we will consider the applications of such an acyclic model.