{"acknowledgement":"This research was partially supported by the Defense Advanced Research Projects Agency (DARPA) under grant HR0011-05-1-0007.","oa_version":"None","abstract":[{"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.","lang":"eng"}],"intvolume":" 11","month":"06","publisher":"Springer","quality_controlled":"1","scopus_import":1,"publication":"Foundations of Computational Mathematics","language":[{"iso":"eng"}],"day":"01","year":"2011","publication_status":"published","date_created":"2018-12-11T12:02:59Z","issue":"3","doi":"10.1007/s10208-010-9081-1","date_published":"2011-06-01T00:00:00Z","volume":11,"page":"305 - 336","_id":"3378","status":"public","type":"journal_article","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T07:43:04Z","citation":{"chicago":"Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics. Springer, 2011. https://doi.org/10.1007/s10208-010-9081-1.","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.” Foundations of Computational Mathematics, vol. 11, no. 3, Springer, 2011, pp. 305–36, doi:10.1007/s10208-010-9081-1.","apa":"Bendich, P., & Harer, J. (2011). Persistent intersection homology. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-010-9081-1","ama":"Bendich P, Harer J. Persistent intersection homology. Foundations of Computational Mathematics. 2011;11(3):305-336. doi:10.1007/s10208-010-9081-1","ieee":"P. Bendich and J. Harer, “Persistent intersection homology,” Foundations of Computational Mathematics, vol. 11, no. 3. Springer, pp. 305–336, 2011.","short":"P. Bendich, J. Harer, Foundations of Computational Mathematics 11 (2011) 305–336."},"department":[{"_id":"HeEd"}],"title":"Persistent intersection homology","author":[{"id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","first_name":"Paul","full_name":"Bendich, Paul","last_name":"Bendich"},{"last_name":"Harer","full_name":"Harer, John","first_name":"John"}],"publist_id":"3229"}