caa a22 4500 445331585 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s10208-010-9081-1 doi (NATIONALLICENCE)springer-10.1007/s10208-010-9081-1 Persistent Intersection Homology [Elektronische Daten] [Paul Bendich, John Harer] 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. SFoCM, 2010 Persistence nationallicence Intersection homology nationallicence Algorithms nationallicence Stratified spaces nationallicence Bendich Paul IST Austria (Institute for Science and Technology Austria), Klosterneuburg, Austria aut Harer John Departments of Mathematics and of Computer Science, and the Center for Systems Biology, Duke University, Durham, NC, USA aut Foundations of Computational Mathematics Springer-Verlag 11/3(2011-06-01), 305-336 1615-3375 11:3<305 2011 11 10208 https://doi.org/10.1007/s10208-010-9081-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-010-9081-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bendich Paul IST Austria (Institute for Science and Technology Austria), Klosterneuburg, Austria aut NATIONALLICENCE 700 1- Harer John Departments of Mathematics and of Computer Science, and the Center for Systems Biology, Duke University, Durham, NC, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/3(2011-06-01), 305-336 1615-3375 11:3<305 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer