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Persistent Intersection Homology

Publication ,  Journal Article
Bendich, P; Harer, J
Published in: Foundations of Computational Mathematics
June 1, 2011

The theory of intersection homology was developed to study the singularities of a topologically stratified space. This paper incorporates this theory into the already developed framework of persistent homology. We demonstrate that persistent intersection homology gives useful information about the relationship between an embedded stratified space and its singularities. We give an algorithm for the computation of the persistent intersection homology groups of a filtered simplicial complex equipped with a stratification by subcomplexes, and we prove its correctness. We also derive, from Poincaré Duality, some structural results about persistent intersection homology. © 2010 SFoCM.

Duke Scholars

Published In

Foundations of Computational Mathematics

DOI

EISSN

1615-3383

ISSN

1615-3375

Publication Date

June 1, 2011

Volume

11

Issue

3

Start / End Page

305 / 336

Related Subject Headings

  • Numerical & Computational Mathematics
  • 49 Mathematical sciences
  • 46 Information and computing sciences
  • 08 Information and Computing Sciences
  • 01 Mathematical Sciences
 

Citation

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MLA
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Bendich, P., & Harer, J. (2011). Persistent Intersection Homology. Foundations of Computational Mathematics, 11(3), 305–336. https://doi.org/10.1007/s10208-010-9081-1
Bendich, P., and J. Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics 11, no. 3 (June 1, 2011): 305–36. https://doi.org/10.1007/s10208-010-9081-1.
Bendich P, Harer J. Persistent Intersection Homology. Foundations of Computational Mathematics. 2011 Jun 1;11(3):305–36.
Bendich, P., and J. Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics, vol. 11, no. 3, June 2011, pp. 305–36. Scopus, doi:10.1007/s10208-010-9081-1.
Bendich P, Harer J. Persistent Intersection Homology. Foundations of Computational Mathematics. 2011 Jun 1;11(3):305–336.
Journal cover image

Published In

Foundations of Computational Mathematics

DOI

EISSN

1615-3383

ISSN

1615-3375

Publication Date

June 1, 2011

Volume

11

Issue

3

Start / End Page

305 / 336

Related Subject Headings

  • Numerical & Computational Mathematics
  • 49 Mathematical sciences
  • 46 Information and computing sciences
  • 08 Information and Computing Sciences
  • 01 Mathematical Sciences