Graphs and Their Clique Complexes Are Pseudotopological Weakly Homotopy Equivalent

2024/05/31 by Jonathan Treviño-Marroquín, Treviño-Marroquín, Jonathan
Computer Science · Mathematics · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.GN

paper · pdf · doi:10.48550/arxiv.2406.00149

openalex publication_date 2024/05/31 · openalex created_date 2024/06/06 · openalex updated_date 2026/07/28

Abstract

We establish a connection between the graphs and their geometric realizations of their clique complexes, proving that graphs with their canonical pseudotopological structure, are weakly homotopy equivalent to the geometric realization of their clique complex.

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