[{"title":"Persistent intersection homology","date_updated":"2025-09-30T08:53:15Z","author":[{"first_name":"Paul","last_name":"Bendich","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","full_name":"Bendich, Paul"},{"full_name":"Harer, John","first_name":"John","last_name":"Harer"}],"abstract":[{"lang":"eng","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."}],"publist_id":"3229","day":"01","citation":{"apa":"Bendich, P., &#38; Harer, J. (2011). Persistent intersection homology. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-010-9081-1\">https://doi.org/10.1007/s10208-010-9081-1</a>","ieee":"P. Bendich and J. Harer, “Persistent intersection homology,” <i>Foundations of Computational Mathematics</i>, vol. 11, no. 3. Springer, pp. 305–336, 2011.","ista":"Bendich P, Harer J. 2011. Persistent intersection homology. Foundations of Computational Mathematics. 11(3), 305–336.","chicago":"Bendich, Paul, and John Harer. “Persistent Intersection Homology.” <i>Foundations of Computational Mathematics</i>. Springer, 2011. <a href=\"https://doi.org/10.1007/s10208-010-9081-1\">https://doi.org/10.1007/s10208-010-9081-1</a>.","mla":"Bendich, Paul, and John Harer. “Persistent Intersection Homology.” <i>Foundations of Computational Mathematics</i>, vol. 11, no. 3, Springer, 2011, pp. 305–36, doi:<a href=\"https://doi.org/10.1007/s10208-010-9081-1\">10.1007/s10208-010-9081-1</a>.","short":"P. Bendich, J. Harer, Foundations of Computational Mathematics 11 (2011) 305–336.","ama":"Bendich P, Harer J. Persistent intersection homology. <i>Foundations of Computational Mathematics</i>. 2011;11(3):305-336. doi:<a href=\"https://doi.org/10.1007/s10208-010-9081-1\">10.1007/s10208-010-9081-1</a>"},"intvolume":"        11","volume":11,"acknowledgement":"This research was partially supported by the Defense Advanced Research Projects Agency (DARPA) under grant HR0011-05-1-0007.","external_id":{"isi":["000290038800002"]},"article_processing_charge":"No","year":"2011","date_created":"2018-12-11T12:02:59Z","language":[{"iso":"eng"}],"publication":"Foundations of Computational Mathematics","publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Springer","type":"journal_article","month":"06","isi":1,"scopus_import":"1","_id":"3378","oa_version":"None","page":"305 - 336","date_published":"2011-06-01T00:00:00Z","status":"public","issue":"3","corr_author":"1","quality_controlled":"1","doi":"10.1007/s10208-010-9081-1","fulldoi":"https://doi.org/10.1007/s10208-010-9081-1","department":[{"_id":"HeEd"}]}]