This research establishes persistent cohomology operations and sharper Gromov-Hausdorff estimates from Riemannian pseudomanifolds.
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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Medina-Mardones et al. (2025) studied this question.
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