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math.AT2025
Doughnut or Mickey Mouse? Detecting Toroidal Structure in Data through Persistent Cup-Length
Ekaterina S. Ivshina, Galit Anikeeva, Ling Zhou
Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies bas…
math.AT2025
Persistence and Topological Complexity
Facundo Mémoli, Ling Zhou
Topological complexity is a homotopy invariant that measures the minimal number of continuous rules required for motion planning in a space. In this work, we introduce persistent a…
math.AT2025
Persistent cohomology operations and Gromov-Hausdorff estimates
Anibal M. Medina-Mardones, Ling Zhou
We establish the foundations of the theory of persistent cohomology operations, derive decomposition formulas for wedge sums and products, and prove their Gromov-Hausdorff stabilit…