Persistent cohomology operations and Gromov-Hausdorff estimates
Algebraic Topology
2025-03-27 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2503.17130,
title = {Persistent cohomology operations and Gromov-Hausdorff estimates},
author = {Anibal M. Medina-Mardones and Ling Zhou},
journal= {arXiv preprint arXiv:2503.17130},
year = {2025}
}
Comments
32 pages, 3 figures