Finite presentation of finitely determined modules

2023/01/20 by Hyry, Eero, Klemetti, Markus
#13E15 #55N31 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.08538

Abstract

In this article we study certain notions of `tameness' for the persistence modules studied in topological data analysis. In particular, we show that after adding infinitary points the so called finitely determined modules become finitely presented.

Related

• The observable structure of persistence modules
• Realizations of Indecomposable Persistence Modules of Arbitrarily Large\n Dimension
• The structure and stability of persistence modules
• Flat covers and injective hulls of persistence modules
• Data structures for real multiparameter persistence modules