Rigidity of terminal simplices in persistent homology

Franc, Aleksandra (author), Virk, Žiga (author)

Given a filtration function on a finite simplicial complex, stability theorem of persistent homology states that the corresponding barcode is continuous with respect to changes in the filtration function. However, due to the discrete setting of simplicial complexes, the simplices terminating matched bars cannot change continuously for arbitrary perturbations of filtration functions. In this paper we provide a sufficient condition for rigidity of a terminal simplex, i.e., a condition on ε > 0 implying that the terminal simplex of a homology class or a bar in persistent homology remains constant through ε-perturbations of filtration function. The condition for a homology class or a bar in dimension n depends only on the barcodes in dimensions n and n + 1.

• Language: English
• Keywords: persistent homology, stability theorem, terminal simplex, rigidity
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FRI - Faculty of Computer and Information Science
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 16 str.
• Numbering: Vol. 117, iss. 4, art. 141
• PID: 20.500.12556/RUL-148271
• UDC: 51
• ISSN on article: 1578-7303
• DOI: 10.1007/s13398-023-01473-z
• COBISS.SI-ID: 157780483
• Publication date in RUL: 09.08.2023

Record is a part of a journal

• Title: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas
• Shortened title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.
• Publisher: Springer Nature, Real Academia de Ciencias Exactas, Físicas y Naturales
• ISSN: 1578-7303
• COBISS.SI-ID: 17645351

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: vztrajna homologija, izrek o stabilnosti, končni simpleks, togost