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.