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G-invariant Persistent Homology

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

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Abstract

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
DOI:10.6092/unibo/amsacta/3614
Depositato da:Patrizio Frosini
Depositato il:05 Dec 2012 08:26
Last modified:19 Dec 2012 15:26

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