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.
ASJC Scopus subject areas
- Geometry and Topology
- Computer Science Applications
- Computational Theory and Mathematics
Fields of Expertise
- Information, Communication & Computing