Foundations of Computational Mathematics

, Volume 11, Issue 3, pp 305–336 | Cite as

Persistent Intersection Homology

  • Paul BendichEmail author
  • John Harer


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.


Persistence Intersection homology Algorithms Stratified spaces 

Mathematics Subject Classification (2000)

55N33 68 


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Copyright information

© SFoCM 2010

Authors and Affiliations

  1. 1.IST Austria (Institute for Science and Technology Austria)KlosterneuburgAustria
  2. 2.Departments of Mathematics and of Computer Science, and the Center for Systems BiologyDuke UniversityDurhamUSA

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