---
_id: '3377'
abstract:
- lang: eng
text: 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.
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.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Dmitriy
full_name: Morozov, Dmitriy
last_name: Morozov
- first_name: Amit
full_name: Patel, Amit
id: 34A254A0-F248-11E8-B48F-1D18A9856A87
last_name: Patel
citation:
ama: 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
apa: Edelsbrunner, H., Morozov, D., & Patel, A. (2011). Quantifying transversality
by measuring the robustness of intersections. Foundations of Computational
Mathematics. Springer. https://doi.org/10.1007/s10208-011-9090-8
chicago: Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “Quantifying Transversality
by Measuring the Robustness of Intersections.” Foundations of Computational
Mathematics. Springer, 2011. https://doi.org/10.1007/s10208-011-9090-8.
ieee: H. Edelsbrunner, D. Morozov, and A. Patel, “Quantifying transversality by
measuring the robustness of intersections,” Foundations of Computational Mathematics,
vol. 11, no. 3. Springer, pp. 345–361, 2011.
ista: Edelsbrunner H, Morozov D, Patel A. 2011. Quantifying transversality by measuring
the robustness of intersections. Foundations of Computational Mathematics. 11(3),
345–361.
mla: 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.
short: H. Edelsbrunner, D. Morozov, A. Patel, Foundations of Computational Mathematics
11 (2011) 345–361.
date_created: 2018-12-11T12:02:59Z
date_published: 2011-06-01T00:00:00Z
date_updated: 2021-01-12T07:43:04Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10208-011-9090-8
intvolume: ' 11'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/0911.2142
month: '06'
oa: 1
oa_version: Submitted Version
page: 345 - 361
publication: Foundations of Computational Mathematics
publication_status: published
publisher: Springer
publist_id: '3230'
quality_controlled: '1'
scopus_import: 1
status: public
title: Quantifying transversality by measuring the robustness of intersections
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2011'
...