Local characterizations for decomposability of 2parameter persistence modules
Abstract
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 2parameter persistence in topological data analysis. Our indecomposables of interest belong to the socalled 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 DOI:
 10.48550/arXiv.2008.02345
 arXiv:
 arXiv:2008.02345
 Bibcode:
 2020arXiv200802345B
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Topology
 EPrint:
 Accepted in Algebras and Representation Theory. 44 pages. Proofs and exposition simplified. We thank the anonymous referees for their invaluable comments