Alma Mater Digital Library

Edited by Documentary and Departmental Support

cambia la lingua in italiano
AMS Acta
ISSN: 2038-7954
Contributi di ricerca dell'Alma Mater Studiorum - Università di Bologna
Informazioni sul Single Sign-On di Ateneo Login for authors

G-invariant Persistent Homology

Frosini, Patrizio (2012) G-invariant Persistent Homology. [Preprint]


Esiste un'altra versione di questo documento. Clicca qui per vederla.

Full text disponibile come:

[img]PDF (G-invariant Persistent Homology)
Available under License Creative Commons Attribution Non-commercial (CC BY-NC 3.0).



Classical persistent homology is not tailored to study the action of transformation groups different from the group Homeo(X) of all self-homeomorphisms of a topological space X. In order to obtain better lower bounds for the natural pseudo-distance d_G associated with a subgroup G of Homeo(X), we need to adapt persistent homology and consider G-invariant persistent homology. Roughly speaking, the main idea consists in defining persistent homology by means of a set of chains that is invariant under the action of G. In this paper we formalize this idea, and prove the stability of G-invariant persistent homology with respect to the natural pseudo-distance d_G. We also show how G-invariant persistent homology could be used in applications concerning shape comparison.

Document type:Preprint
Uncontrolled Keywords:Natural pseudo-distance, filtering function, group action, lower bound, stability, shape comparison
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/03 Geometria
Depositato da:Patrizio Frosini
Depositato il:05 Dec 2012 08:26
Last modified:19 Dec 2012 15:26

Versioni disponibili di questo documento

Solo per lo Staff dell Archivio: Gestione del documento