Persistent intersection homology Journal Article

Author(s): Bendich, Paul; Harer, John
Article Title: Persistent intersection homology
Affiliation IST Austria
Abstract: 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.
Journal Title: Foundations of Computational Mathematics
Volume: 11
Issue 3
ISSN: 1615-3383
Publisher: Springer  
Date Published: 2011-01-01
Start Page: 305
End Page: 336
Sponsor: This research was partially supported by the Defense Advanced Research Projects Agency (DARPA) under grant HR0011-05-1-0007.
DOI: 10.1007/s10208-010-9081-1
Open access: no
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