Quantifying transversality by measuring the robustness of intersections

H. Edelsbrunner, D. Morozov, A. Patel, Foundations of Computational Mathematics 11 (2011) 345–361.


Journal Article | Published | English
Department
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.
Publishing Year
Date Published
2011-06-01
Journal Title
Foundations of Computational Mathematics
Acknowledgement
This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0007 and HR0011-05-1-0057.
Volume
11
Issue
3
Page
345 - 361
IST-REx-ID

Cite this

Edelsbrunner H, Morozov D, Patel A. Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. 2011;11(3):345-361. doi:10.1007/s10208-011-9090-8
Edelsbrunner, H., Morozov, D., & Patel, A. (2011). Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics, 11(3), 345–361. https://doi.org/10.1007/s10208-011-9090-8
Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “Quantifying Transversality by Measuring the Robustness of Intersections.” Foundations of Computational Mathematics 11, no. 3 (2011): 345–61. https://doi.org/10.1007/s10208-011-9090-8.
H. Edelsbrunner, D. Morozov, and A. Patel, “Quantifying transversality by measuring the robustness of intersections,” Foundations of Computational Mathematics, vol. 11, no. 3, pp. 345–361, 2011.
Edelsbrunner H, Morozov D, Patel A. 2011. Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. 11(3), 345–361.
Edelsbrunner, Herbert, et al. “Quantifying Transversality by Measuring the Robustness of Intersections.” Foundations of Computational Mathematics, vol. 11, no. 3, Springer, 2011, pp. 345–61, doi:10.1007/s10208-011-9090-8.

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