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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…
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…
Algebraic Zhou valuations
Shijie Bao, Qi'an Guan, Lin Zhou
In this paper, we generalize Zhou valuations, originally defined on complex domains, to the framework of general schemes. We demonstrate that an algebraic version of the Jonsson--M…
Torsion higher Chow cycles modulo
Theodosis Alexandrou, Lin Zhou
We study the injectivity property of certain actions of higher Chow groups on refined unramified cohomology. As an application for every and for each and $n\ge…
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…