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Computational Tools in Weighted Persistent Homology (1711.09211v3)

Published 25 Nov 2017 in math.AT

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 $p2$ weighted persistent homology given some information on the mod $p$ weighted persistent homology.

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