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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2601.03275 |
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Table des matières:
- The well groups were introduced by Edelsbrunner, Morozov, and Patel to measure the robustness of geometric features of a function with respect to perturbations. Roughly speaking, the $r$-th well group measures the number of features that cannot be removed by perturbing the function by at most $r$. The Shrinking Wellness Lemma states that the rank of these groups decreases as $r$ increases. In the generality originally stated, it is wrong. We present a counterexample and give conditions under which the result holds. These conditions are general enough to cover most cases in which the well groups have been applied.