Persistent cohomology operations and Gromov-Hausdorff estimates

Anibal M.Medina-Mardones; Ling Zhou

Persistent cohomology operations and Gromov-Hausdorff estimates

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arxiv 2503.17130 v2 pith:VOG2D2OE submitted 2025-03-21 math.AT

Anibal M.Medina-Mardones , Ling Zhou This is my paper · ORCID

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keywords persistentcohomologygromov-hausdorffoperationsestimatesconstructdecompositionderive

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We establish the foundations of the theory of persistent cohomology operations, derive decomposition formulas for wedge sums and products, and prove their Gromov-Hausdorff stability. We use these results to construct pairs of Riemannian pseudomanifolds for which the Gromov-Hausdorff estimates derived from persistent cohomology operations are strictly sharper than those obtained using persistent homology.

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Persistence and Topological Complexity
math.AT 2025-06 conditional novelty 6.0 of 10

Persistent topological complexity and persistent zero-divisor-cup-length are defined, shown stable under homotopy interleaving and Vietoris-Rips perturbations, and used to recover a Gromov-Hausdorff lower bound of pi/...

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