--- res: bibo_abstract: - We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining collections of interrelated sorted lists together with their persistence diagrams. @eng bibo_authorlist: - foaf_Person: foaf_givenName: Ranita foaf_name: Biswas, Ranita foaf_surname: Biswas foaf_workInfoHomepage: http://www.librecat.org/personId=3C2B033E-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-5372-7890 - foaf_Person: foaf_givenName: Sebastiano foaf_name: Cultrera di Montesano, Sebastiano foaf_surname: Cultrera di Montesano foaf_workInfoHomepage: http://www.librecat.org/personId=34D2A09C-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-6249-0832 - foaf_Person: foaf_givenName: Herbert foaf_name: Edelsbrunner, Herbert foaf_surname: Edelsbrunner foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9823-6833 - foaf_Person: foaf_givenName: Morteza foaf_name: Saghafian, Morteza foaf_surname: Saghafian dct_date: 2022^xs_gYear dct_language: eng dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@ dct_title: 'A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs@' ...