2025/03/21 by Anibal M. Medina-Mardones, Ling Zhou, Medina-Mardones, Anibal M. +1 · 1 citation
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2503.17130
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.