Computational Tools in Weighted Persistent Homology

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 $p^2$ weighted persistent homology given some information on the mod $p$ weighted persistent homology.

20 pages

References in corpus (2)

• Defining and computing persistent Z-homology in the general case
• Balanced complexes and effective divisors on ${\overline{M}}_{0,n}$

Cited by in corpus (5)

• Discrete Morse Theory for Weighted Simplicial Complexes
• Weighted (Co)homology and Weighted Laplacian
• Hodge Decompositions for Weighted Hypergraphs
• Weighted Path homology of Weighted Digraphs and Persistence
• Weighted Fundamental Group