Year: 2019
Type: preprint
Abstract: We define and study several new interleaving distances for persistent cohomology which take into account the algebraic structures of the cohomology of a space, for instance the cup product or the action of the Steenrod algebra. In particular, we prove that there exists a persistent A-infinity-structure associated to data sets and and we define the associated distance. We prove the stability of these new distances for Cech or Vietoris Rips complexes with respect to the Gromov-Hausdorff distance, and we compare these new distances with each other and the classical one, building some examples which prove that they are not equal in general and refine effectively the classical bottleneck distance.
Source: arXiv (Cornell University)
Authors: Ginot, Grégory, Leray, Johan
Institution: Laboratoire Analyse, Géométrie et Applications
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2947417463