Abstract
While persistent homology has taken strides towards becoming a widespread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and complete descriptor analo-gous to the persistence diagrams of the former. We propose a simple algebraic construction to illustrate the existence of infinite families of indecomposable persistence modules over reg-ular commutative grids of sufficient size. On top of providing a constructive proof that those commutative grids are representation-infinite, we also provide realizations of the modules by topological spaces and Vietoris-Rips filtrations, showing that they can actually appear in real data and are not the product of degeneracies.
Original language | English |
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Pages (from-to) | 298-326 |
Number of pages | 29 |
Journal | Journal of Computational Geometry |
Volume | 13 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2022 |
ASJC Scopus subject areas
- Geometry and Topology
- Computer Science Applications
- Computational Theory and Mathematics
Fields of Expertise
- Information, Communication & Computing