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 weighted persistent homology given some information on the mod weighted persistent homology.
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