Persistent intersection homology
Bendich P, Harer J. 2011. Persistent intersection homology. Foundations of Computational Mathematics. 11(3), 305–336.
Download
No fulltext has been uploaded. References only!
Journal Article
| Published
| English
Scopus indexed
Author
Bendich, PaulISTA;
Harer, John
Department
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.
Publishing Year
Date Published
2011-06-01
Journal Title
Foundations of Computational Mathematics
Publisher
Springer
Acknowledgement
This research was partially supported by the Defense Advanced Research Projects Agency (DARPA) under grant HR0011-05-1-0007.
Volume
11
Issue
3
Page
305 - 336
IST-REx-ID
Cite this
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. Springer. https://doi.org/10.1007/s10208-010-9081-1
Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics. Springer, 2011. 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. Springer, 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.