2025/02/04 by Joaquín Díaz Boïls, Boils, Joaquin Diaz
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Biological sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Neurons and Cognition (q-bio.NC) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2502.02151
openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A multicomplex structure is defined from an ordered lattice of multigraphs. This structure will help us to observe the features of Persistent Homology in this context, its interaction with the ordering and the repercussions of the process of merging multigraphs in the calculation of the Betti numbers. For the latter, an extended version of the incremental algorithm is provided. The ideas here developed are mainly oriented to the original example described in [10] and used more extensively in [11] in the context of the formalization of the notion of embodiment in Neuroscience.