---
_id: '3378'
abstract:
- lang: eng
  text: The theory of intersection homology was developed to study the singularities
    of a topologically stratified space. This paper in- corporates this theory into
    the already developed framework of persistent homology. We demonstrate that persistent
    intersec- tion homology gives useful information about the relationship between
    an embedded stratified space and its singularities. We give, and prove the correctness
    of, an algorithm for the computa- tion of the persistent intersection homology
    groups of a filtered simplicial complex equipped with a stratification by subcom-
    plexes. We also derive, from Poincare ́ Duality, some structural results about
    persistent intersection homology.
acknowledgement: This research was partially supported by the Defense Advanced Research
  Projects Agency (DARPA) under grant HR0011-05-1-0007.
article_processing_charge: No
author:
- first_name: Paul
  full_name: Bendich, Paul
  id: 43F6EC54-F248-11E8-B48F-1D18A9856A87
  last_name: Bendich
- first_name: John
  full_name: Harer, John
  last_name: Harer
citation:
  ama: Bendich P, Harer J. Persistent intersection homology. <i>Foundations of Computational
    Mathematics</i>. 2011;11(3):305-336. doi:<a href="https://doi.org/10.1007/s10208-010-9081-1">10.1007/s10208-010-9081-1</a>
  apa: Bendich, P., &#38; Harer, J. (2011). Persistent intersection homology. <i>Foundations
    of Computational Mathematics</i>. Springer. <a href="https://doi.org/10.1007/s10208-010-9081-1">https://doi.org/10.1007/s10208-010-9081-1</a>
  chicago: Bendich, Paul, and John Harer. “Persistent Intersection Homology.” <i>Foundations
    of Computational Mathematics</i>. Springer, 2011. <a href="https://doi.org/10.1007/s10208-010-9081-1">https://doi.org/10.1007/s10208-010-9081-1</a>.
  ieee: P. Bendich and J. Harer, “Persistent intersection homology,” <i>Foundations
    of Computational Mathematics</i>, vol. 11, no. 3. Springer, pp. 305–336, 2011.
  ista: Bendich P, Harer J. 2011. Persistent intersection homology. Foundations of
    Computational Mathematics. 11(3), 305–336.
  mla: Bendich, Paul, and John Harer. “Persistent Intersection Homology.” <i>Foundations
    of Computational Mathematics</i>, vol. 11, no. 3, Springer, 2011, pp. 305–36,
    doi:<a href="https://doi.org/10.1007/s10208-010-9081-1">10.1007/s10208-010-9081-1</a>.
  short: P. Bendich, J. Harer, Foundations of Computational Mathematics 11 (2011)
    305–336.
corr_author: '1'
date_created: 2018-12-11T12:02:59Z
date_published: 2011-06-01T00:00:00Z
date_updated: 2025-09-30T08:53:15Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10208-010-9081-1
external_id:
  isi:
  - '000290038800002'
fulldoi: https://doi.org/10.1007/s10208-010-9081-1
intvolume: '        11'
isi: 1
issue: '3'
language:
- iso: eng
month: '06'
oa_version: None
page: 305 - 336
publication: Foundations of Computational Mathematics
publication_status: published
publisher: Springer
publist_id: '3229'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Persistent intersection homology
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 11
year: '2011'
...