caa a22 4500 445331593 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s10208-011-9090-8 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9090-8 Quantifying Transversality by Measuring theRobustness of Intersections [Elektronische Daten] [Herbert Edelsbrunner, Dmitriy Morozov, Amit Patel] By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its robustness, the magnitude of a perturbation in this space necessary to kill it, and then we prove that the robustness is stable. Among the applications of this result is a stable notion of robustness for fixed points of continuous mappings and a statement of stability for contours of smooth mappings. SFoCM, 2011 Smooth mappings nationallicence Transversality nationallicence Fixed points nationallicence Contours nationallicence Homology nationallicence Filtrations nationallicence Zigzag modules nationallicence Persistence nationallicence Perturbations nationallicence Stability nationallicence Edelsbrunner Herbert Departments of Computer Science and of Mathematics, Duke University, Durham, NC, USA aut Morozov Dmitriy Departments of Computer Science and of Mathematics, Stanford University, Stanford, CA, USA aut Patel Amit Departments of Computer Science and of Mathematics, Duke University, Durham, NC, USA aut Foundations of Computational Mathematics Springer-Verlag 11/3(2011-06-01), 345-361 1615-3375 11:3<345 2011 11 10208 https://doi.org/10.1007/s10208-011-9090-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9090-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Edelsbrunner Herbert Departments of Computer Science and of Mathematics, Duke University, Durham, NC, USA aut NATIONALLICENCE 700 1- Morozov Dmitriy Departments of Computer Science and of Mathematics, Stanford University, Stanford, CA, USA aut NATIONALLICENCE 700 1- Patel Amit Departments of Computer Science and of Mathematics, Duke University, Durham, NC, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/3(2011-06-01), 345-361 1615-3375 11:3<345 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer