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Publications [#243366] of Paul L Bendich

Papers Published

  1. with Bendich, P; Harer, J, Persistent Intersection Homology, Foundations of Computational Mathematics, vol. 11 no. 3 (2011), pp. 305-336, ISSN 1615-3375 [doi]
    (last updated on 2017/12/17)

    Abstract:
    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 an algorithm for the computation of the persistent intersection homology groups of a filtered simplicial complex equipped with a stratification by subcomplexes, and we prove its correctness. We also derive, from Poincaré Duality, some structural results about persistent intersection homology. © 2010 SFoCM.

 

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