2025/07/28 by Yariana Diaz, Diaz, Yariana
Computer Science · Mathematics · #16G20 #16G70 #18E10 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2507.20483
openalex publication_date 2025/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When filtering a topological space by a single parameter, the theory of quiver representations provides a complete framework for decomposing the resulting persistence module to obtain its barcode. This is achieved by interpreting the persistence module as a representation of a Type \mathbbAn quiver. The complexity increases significantly when filtering by two or more parameters. In particular, multi-parameter persistence typically yields tame or wild type quivers whose indecomposable representations are more complicated to describe and for which arbitrary representations are much more difficult to decompose. The theme of this work is to provide a framework for restricting to subcategories of quiver representations whose objects can be distinguished from one another through computational means.