English

Computational Tools in Weighted Persistent Homology

Algebraic Topology 2019-07-17 v3

Abstract

In this paper, we study further properties and applications of weighted homology and persistent homology. We introduce the Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology. For applications, we show an algorithm to construct a filtration of weighted simplicial complexes from a weighted network. We also prove a theorem that allows us to calculate the mod p2p^2 weighted persistent homology given some information on the mod pp weighted persistent homology.

Keywords

Cite

@article{arxiv.1711.09211,
  title  = {Computational Tools in Weighted Persistent Homology},
  author = {Shiquan Ren and Chengyuan Wu and Jie Wu},
  journal= {arXiv preprint arXiv:1711.09211},
  year   = {2019}
}

Comments

20 pages

R2 v1 2026-06-22T22:56:40.818Z