November 8, 2025Open Access

On empirical Hodge Laplacians under the manifold hypothesis

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Empirical analysis shows error bounds for Dirichlet forms in differential forms, indicating insights into topology.

High-probability error bounds for Dirichlet forms on graph Laplacians improve upon previous work.
The study reveals connections to the Laplace-Beltrami operator and its application in topological data analysis.
Observational analysis focuses on the implications of Betti numbers in the context of spectrum.
Improvements in error bounds may guide applications in manifold learning and geometric inference.

Lerch et al. (2025) studied this question.

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