@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},
}