Quantifying Transversality by Measuring the Robustness of Intersections
Computational Geometry
2010-04-22 v2 General Mathematics
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 perturbations 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.
Keywords
Cite
@article{arxiv.0911.2142,
title = {Quantifying Transversality by Measuring the Robustness of Intersections},
author = {Herbert Edelsbrunner and Dmitriy Morozov and Amit Patel},
journal= {arXiv preprint arXiv:0911.2142},
year = {2010}
}