Quantifying transversality by measuring the robustness of intersections - Edelsbrunner, Herbert; Morozov, Dmitriy; Patel, Amit (Foundations of Computational Mathematics, 2011)
By definition, transverse intersections are stable under in- finitesimal perturbations. Using persistent homology, we ex- tend this notion to sizeable perturbations. Specifically, we assign to each homology class of the intersection its robust- ness, the magnitude of a perturbation necessary to kill it, and prove that robustness is stable. Among the applications of this result is a stable notion of robustness for fixed points of continuous mappings and a statement of stability for con- tours of smooth mappings.
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