English

Weighted Persistent Homology

Algebraic Topology 2019-05-29 v2

Abstract

We introduce weighted versions of the classical \v{C}ech and Vietoris-Rips complexes. We show that a version of the Vietoris-Rips Lemma holds for these weighted complexes and that they enjoy appropriate stability properties. We also give some preliminary applications of these weighted complexes.

Cite

@article{arxiv.1709.00097,
  title  = {Weighted Persistent Homology},
  author = {Greg Bell and Austin Lawson and Joshua Martin and James Rudzinski and Clifford Smyth},
  journal= {arXiv preprint arXiv:1709.00097},
  year   = {2019}
}

Comments

11 pages, 5 figures

R2 v1 2026-06-22T21:29:48.318Z