Quantifying Transversality by Measuring the Robustness of Intersections |
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Authors: | Herbert Edelsbrunner Dmitriy Morozov Amit Patel |
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Institution: | (1) Department of Mathematics, Drexel University, Philadelphia, PA 19104-2875, USA; |
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Abstract: | By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend
this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its robustness,
the magnitude of a perturbation in this space necessary to kill it, and then we prove that the 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 contours of smooth mappings. |
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Keywords: | |
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