Persistence stability for geometric complexes
Algebraic Topology
2013-11-18 v3 Computational Geometry
Abstract
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 precompact 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.
Cite
@article{arxiv.1207.3885,
title = {Persistence stability for geometric complexes},
author = {Frederic Chazal and Vin de Silva and Steve Oudot},
journal= {arXiv preprint arXiv:1207.3885},
year = {2013}
}
Comments
We include a discussion of ambient Cech complexes and a new class of examples called Dowker complexes