2020/08/05 by Magnus Bakke Botnan, Botnan, Magnus Bakke, Vadim Lebovici +3 · 1 citation
Computer Science · #Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2008.02345
openalex publication_date 2020/08/05 · openalex created_date 2022/12/26 · openalex updated_date 2026/07/28
We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets, corresponding to the setting of 2-parameter persistence in topological data analysis. Our indecomposables of interest belong to the so-called interval modules, which by definition are indicator representations of intervals in the poset. While the whole class of interval modules does not admit such a local characterization, we show that the subclass of rectangle modules does admit one and that it is, in some precise sense, the largest subclass to do so.