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| Computational Tools in Weighted Persistent Homology* |
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Citation： |
Shiquan REN,Chengyuan WU,Jie WU.Computational Tools in Weighted Persistent Homology*[J].Chinese Annals of Mathematics B,2021,42(2):237~258 |
| Page view： 859
Net amount： 498 |
Authors： |
Shiquan REN; Chengyuan WU;Jie WU |
Foundation： |
Singapore Ministry of Education Research Grant (AcRF Tier 1 WBS No. R-146-000-222-112), the Postdoctoral International Exchange Program of China 2019 Project from the Office of China Postdoctoral Council, China Postdoctoral Science Foundation, the President’s Graduate Fellowship of National University of Singapore, the Natural Science Foundation of China (Nos. 11971144, 12001310), High-Level Scientific Research Foundation of Hebei Province and China Postdoctoral Science Foundation (No. 2019-2021). |
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| Abstract： |
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 p2 weighted persistent homology provided with some information on the mod p weighted persistent homology. |
Keywords： |
Algebraic topology, Persistent homology, Weighted persistent homology,Bockstein spectral sequence |
Classification： |
55N35, 55T99, 55U20, 55U10 |
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