Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension

Mickaël Buchet, Emerson G. Escolar

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)298-326
Number of pages29
JournalJournal of Computational Geometry
Issue number1
Publication statusPublished - 2022

ASJC Scopus subject areas

  • Geometry and Topology
  • Computer Science Applications
  • Computational Theory and Mathematics

Fields of Expertise

  • Information, Communication & Computing


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