Bendich, PaulIST Austria; Harer, John
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.
Foundations of Computational Mathematics
This research was partially supported by the Defense Advanced Research Projects Agency (DARPA) under grant HR0011-05-1-0007.
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Bendich P, Harer J. Persistent intersection homology. Foundations of Computational Mathematics. 2011;11(3):305-336. doi:10.1007/s10208-010-9081-1
Bendich, P., & Harer, J. (2011). Persistent intersection homology. Foundations of Computational Mathematics, 11(3), 305–336. https://doi.org/10.1007/s10208-010-9081-1
Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics 11, no. 3 (2011): 305–36. https://doi.org/10.1007/s10208-010-9081-1.
P. Bendich and J. Harer, “Persistent intersection homology,” Foundations of Computational Mathematics, vol. 11, no. 3, pp. 305–336, 2011.
Bendich P, Harer J. 2011. Persistent intersection homology. Foundations of Computational Mathematics. 11(3), 305–336.
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.