On the Stability of Interval Decomposable Persistence Modules

Håvard Bakke Bjerkevik

Research output: Contribution to journalArticlepeer-review

Abstract

The algebraic stability theorem for persistence modules is a central result in the theory of stability for persistent homology. We introduce a new proof technique which we use to prove a stability theorem for n-dimensional rectangle decomposable persistence modules up to a constant 2n−1 that generalizes the algebraic stability theorem, and give an example showing that the bound cannot be improved for n=2. We then apply the technique to prove stability for block decomposable modules, from which novel results for zigzag modules and Reeb graphs follow. These results are improvements on weaker bounds in previous work, and the bounds we obtain are optimal.
Original languageEnglish
Pages (from-to)92-121
Number of pages30
JournalDiscrete & Computational Geometry
Volume66
Issue number1
DOIs
Publication statusPublished - 11 Jul 2021

Keywords

  • Multiparameter persistence
  • Persistent homology
  • Reeb graphs
  • Stability
  • Zigzag modules

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Computational Theory and Mathematics

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