David Meyer (1/30/18): Some algebraic stability theorems for generalized persistence modules скачать в хорошем качестве

David Meyer (1/30/18): Some algebraic stability theorems for generalized persistence modules

From an algebraic point of view, generalized persistence modules can be interpreted as finitely-generated modules for a poset algebra. We prove an algebraic analogue of the isometry theorem of Bauer and Lesnick for a large class of posets. This theorem shows that for such posets, the interleaving metric of Bubenik, de Silva and Scott can be realized as a bottleneck metric which incorporates some algebraic information. In another theorem, we show that this perspective is sufficiently general in the sense that if two generalized persistence modules come from data, we can associate to them a directed set of algebras over which they can be compared and can recover their classical interleaving distance by taking limits. In other work, we find minimal conditions for stability when general persistence modules for a quiver are endowed with a bottleneck metric coming from a weighted graph metric on the Auslander-Retien quiver of the module category.