Persistent Intersection Homology

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Bendich, P; Harer, J

Published Date

  • June 1, 2011

Published In

Volume / Issue

  • 11 / 3

Start / End Page

  • 305 - 336

Electronic International Standard Serial Number (EISSN)

  • 1615-3383

International Standard Serial Number (ISSN)

  • 1615-3375

Digital Object Identifier (DOI)

  • 10.1007/s10208-010-9081-1

Citation Source

  • Scopus