Computational Tools in Weighted Persistent Homology
Shiquan Ren , Chengyuan Wu , Jie Wu
Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (2) : 237 -258.
Computational Tools in Weighted Persistent Homology
In this paper, the authors study further properties and applications of weighted homology and persistent homology. The Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology are introduced. For applications, the authors show an algorithm to construct a filtration of weighted simplicial complexes from a weighted network. They also prove a theorem to calculate the mod p 2 weighted persistent homology provided with some information on the mod p weighted persistent homology.
Algebraic topology / Persistent homology / Weighted persistent homology / Bockstein spectral sequence
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