Expectation of topological invariants
Geometric Topology
2022-11-23 v1
Abstract
In this paper, we study the expectation values of topological invariants of the Vietoris-Rips complex and \v{C}ech complex for a finite set of sample points on a Riemannian manifold. We show that the Betti number and Euler characteristic of the complexes are Lipschitz functions of the scale parameter and that there is an interval such that the Betti curve converges to the Betti number of the underlying manifold.
Keywords
Cite
@article{arxiv.2211.12058,
title = {Expectation of topological invariants},
author = {Taejin Paik and Otto van Koert},
journal= {arXiv preprint arXiv:2211.12058},
year = {2022}
}
Comments
9 pages; 1 figure