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2011

Quantifying Transversality by Measuring the Robustness of Intersections

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Quantifying Transversality by Measuring the Robustness of Intersections
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 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 contours of smooth mappings. Communicated by Gunnar Carlsson AMS Subject Classification - 55N99 Keywords. Smooth mappings, transversality, fixed points, contours, homology, filtrations, zigzag modules, persistence, perturbations, stability.
Herbert Edelsbrunner, Dmitriy Morozov, Amit K. Pat
Added 28 Aug 2011
Updated 28 Aug 2011
Type Journal
Year 2011
Where FOCM
Authors Herbert Edelsbrunner, Dmitriy Morozov, Amit K. Patel
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