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math.DG2024
Topology-preserving Hodge Decomposition in the Eulerian Representation
Zhe Su, Yiying Tong, Guo-Wei Wei
The Hodge decomposition is a fundamental result in differential geometry and algebraic topology, particularly in the study of differential forms on a Riemannian manifold. Despite e…
math.DG2024
Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning
Zhe Su, Yiying Tong, Guo-Wei Wei
Recently, topological data analysis has become a trending topic in data science and engineering. However, the key technique of topological data analysis, i.e., persistent homology,…