Persistence stability for geometric complexes

@article{Chazal2012PersistenceSF,
  title={Persistence stability for geometric complexes},
  author={Fr{\'e}d{\'e}ric Chazal and Vin de Silva and Steve Oudot},
  journal={CoRR},
  year={2012},
  volume={abs/1207.3885}
}
In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, Čech 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 Čech complexes… CONTINUE READING
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