{"abstract":[{"lang":"eng","text":"Persistent homology is an algebraic tool for measuring topological features of shapes and functions. It casts the multi-scale organization we frequently observe in nature into a mathematical formalism. Here we give a record of the short history of persistent homology and present its basic concepts. Besides the mathematics we focus on algorithms and mention the various connections to applications, including to biomolecules, biological networks, data analysis, and geometric modeling."}],"year":"2008","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Herbert Edelsbrunner"},{"first_name":"John","last_name":"Harer","full_name":"Harer, John"}],"acknowledgement":"Supported in part by DARPA under grants HR0011-05-1-0007 and HR0011-05-0057 and by the NSF under grant DBI-06-06873.","page":"257 - 282","month":"03","publisher":"American Mathematical Society","type":"book_chapter","alternative_title":["Contemporary Mathematics"],"publist_id":"2156","citation":{"ama":"Edelsbrunner H, Harer J. Persistent homology - a survey. In: <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>. American Mathematical Society; 2008:257-282.","ieee":"H. Edelsbrunner and J. Harer, “Persistent homology - a survey,” in <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>, American Mathematical Society, 2008, pp. 257–282.","mla":"Edelsbrunner, Herbert, and John Harer. “Persistent Homology - a Survey.” <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>, American Mathematical Society, 2008, pp. 257–82.","apa":"Edelsbrunner, H., &#38; Harer, J. (2008). Persistent homology - a survey. In <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i> (pp. 257–282). American Mathematical Society.","chicago":"Edelsbrunner, Herbert, and John Harer. “Persistent Homology - a Survey.” In <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>, 257–82. American Mathematical Society, 2008.","short":"H. Edelsbrunner, J. Harer, in:, Surveys on Discrete and Computational Geometry: Twenty Years Later, American Mathematical Society, 2008, pp. 257–282.","ista":"Edelsbrunner H, Harer J. 2008.Persistent homology - a survey. In: Surveys on Discrete and Computational Geometry: Twenty Years Later. Contemporary Mathematics, , 257–282."},"quality_controlled":0,"title":"Persistent homology - a survey","date_created":"2018-12-11T12:06:11Z","status":"public","date_updated":"2021-01-12T07:53:33Z","date_published":"2008-03-28T00:00:00Z","day":"28","extern":1,"publication":"Surveys on Discrete and Computational Geometry: Twenty Years Later","_id":"3969","publication_status":"published"}