article published yes Paul Bendich author 43F6EC54-F248-11E8-B48F-1D18A9856A87 John Harer author HeEd department 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. Springer2011 eng 00029003880000210.1007/s10208-010-9081-1 113305 - 336 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>. P. Bendich, J. Harer, Foundations of Computational Mathematics 11 (2011) 305–336. 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>. Bendich P, Harer J. 2011. Persistent intersection homology. Foundations of Computational Mathematics. 11(3), 305–336. P. Bendich and J. Harer, “Persistent intersection homology,” <i>Foundations of Computational Mathematics</i>, vol. 11, no. 3. Springer, pp. 305–336, 2011. 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> 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> 33782018-12-11T12:02:59Z2025-09-30T08:53:15Z