Persistent Intersection Homology

The theory of intersection homology was developed to study the singularities of a topologically stratified space. This paper incorporates this theory into the already developed framework of persistent homology. We demonstrate that persistent intersection 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 computation of the persistent intersection homology groups of a filtered simplicial complex equipped with a stratification by subcomplexes. We also derive, from Poincar´e Duality, some structural results about persistent intersection homology. AMS Subject Classifications 55N33, 68.

• Type: Journal
• Year: 2011
• Where: FOCM
• Authors: Paul Bendich, John Harer
• Keywords: Classi, FOCM 2011, Formal Methods, Homology, Singularities