Topological persistence of configuration spaces and independence complexes for digraphs

2025/04/21 by Shiquan Ren, Ren, Shiquan
Computer Science · #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2504.15126

openalex publication_date 2025/04/21 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We study the topological persistence of the (path) configuration spaces and the (path) independence complexes for digraphs as well as their underlying graphs. We construct some canonical embeddings from the (path) independence complexes of the underlying graphs to the (path) independence complexes of the digraphs as well as some canonical embeddings between the (path) independence complexes induced by strong totally geodesic immersions and strong totally geodesic embeddings of (di)graphs. We apply the path homology to the path independence complexes of (di)graphs. As by-products, we derive some consequences about the Shannon capacities.

Citations

• Persistent bundles over configuration spaces and obstructions for regular embeddings
• Double complexes for configuration spaces and hypergraphs on manifolds
• The topological complexity of pure graph braid groups is stably maximal
• Orders of the canonical vector bundles over configuration spaces of finite graphs
• On the homology of independence complexes
• The Embedded Homology of Hypergraphs and Applications
• Homotopy theory for digraphs
• Homologies of path complexes and digraphs
• Min-type Morse theory for configuration spaces of hard spheres
• The Shannon capacity of a graph and the independence numbers of its powers
• Embeddings With Multiple Regularity

Related

• Independence complexes of wedge of graphs
• Stability of persistent path homology of path complexes
• Matching and Independence Complexes Related to Small Grids
• On independence complexes of graph products
• On the homology of independence complexes