---
_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.
article_processing_charge: No
arxiv: 1
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. <i>Foundations of Computational Mathematics</i>.
    2011;11(3):345-361. doi:<a href="https://doi.org/10.1007/s10208-011-9090-8">10.1007/s10208-011-9090-8</a>
  apa: Edelsbrunner, H., Morozov, D., &#38; Patel, A. (2011). Quantifying transversality
    by measuring the robustness of intersections. <i>Foundations of Computational
    Mathematics</i>. Springer. <a href="https://doi.org/10.1007/s10208-011-9090-8">https://doi.org/10.1007/s10208-011-9090-8</a>
  chicago: Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “Quantifying Transversality
    by Measuring the Robustness of Intersections.” <i>Foundations of Computational
    Mathematics</i>. Springer, 2011. <a href="https://doi.org/10.1007/s10208-011-9090-8">https://doi.org/10.1007/s10208-011-9090-8</a>.
  ieee: H. Edelsbrunner, D. Morozov, and A. Patel, “Quantifying transversality by
    measuring the robustness of intersections,” <i>Foundations of Computational Mathematics</i>,
    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.” <i>Foundations of Computational Mathematics</i>,
    vol. 11, no. 3, Springer, 2011, pp. 345–61, doi:<a href="https://doi.org/10.1007/s10208-011-9090-8">10.1007/s10208-011-9090-8</a>.
  short: H. Edelsbrunner, D. Morozov, A. Patel, Foundations of Computational Mathematics
    11 (2011) 345–361.
corr_author: '1'
date_created: 2018-12-11T12:02:59Z
date_published: 2011-06-01T00:00:00Z
date_updated: 2025-09-30T08:53:52Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10208-011-9090-8
external_id:
  arxiv:
  - '0911.2142'
  isi:
  - '000290038800004'
intvolume: '        11'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 11
year: '2011'
...