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Article Dans Une Revue Geometriae Dedicata Année : 2014

Persistence Stability for Geometric complexes

Résumé

In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, Cech and witness complexes) built on top of totally bounded metric spaces. Using recent developments in the theory of topological persistence, we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov–Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and Cech complexes built on top of compact spaces.

Dates et versions

hal-00923560 , version 1 (03-01-2014)

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Citer

Frédéric Chazal, Vin de Silva, Steve Y. Oudot. Persistence Stability for Geometric complexes. Geometriae Dedicata, 2014, 173, pp.193-214. ⟨10.1007/s10711-013-9937-z⟩. ⟨hal-00923560⟩

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