@article{3377, abstract = {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.}, author = {Edelsbrunner, Herbert and Morozov, Dmitriy and Patel, Amit}, journal = {Foundations of Computational Mathematics}, number = {3}, pages = {345 -- 361}, publisher = {Springer}, title = {{Quantifying transversality by measuring the robustness of intersections}}, doi = {10.1007/s10208-011-9090-8}, volume = {11}, year = {2011}, }