TY - JOUR AB - 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. AU - Edelsbrunner, Herbert AU - Morozov, Dmitriy AU - Patel, Amit ID - 3377 IS - 3 JF - Foundations of Computational Mathematics TI - Quantifying transversality by measuring the robustness of intersections VL - 11 ER -