TY - JOUR
AB - 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.
AU - Bendich, Paul
AU - Harer, John
ID - 3378
IS - 3
JF - Foundations of Computational Mathematics
TI - Persistent intersection homology
VL - 11
ER -