{"page":"1011 - 1020","abstract":[{"text":"Motivated by the measurement of local homology and of functions on noisy domains, we extend the notion of persistent homology to sequences of kernels, images, and cokernels of maps induced by inclusions in a filtration of pairs of spaces. Specifically, we note that persistence in this context is well defined, we prove that the persistence diagrams are stable, and we explain how to compute them.","lang":"eng"}],"author":[{"full_name":"Cohen-Steiner, David","first_name":"David","last_name":"Cohen Steiner"},{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Herbert Edelsbrunner","orcid":"0000-0002-9823-6833"},{"full_name":"Harer, John","last_name":"Harer","first_name":"John"},{"last_name":"Morozov","first_name":"Dmitriy","full_name":"Morozov, Dmitriy"}],"year":"2009","publist_id":"2159","type":"conference","month":"01","publisher":"SIAM","status":"public","conference":{"name":"SODA: Symposium on Discrete Algorithms"},"date_published":"2009-01-01T00:00:00Z","date_updated":"2021-01-12T07:53:32Z","title":"Persistent homology for kernels, images, and cokernels","quality_controlled":0,"citation":{"ama":"Cohen Steiner D, Edelsbrunner H, Harer J, Morozov D. Persistent homology for kernels, images, and cokernels. In: SIAM; 2009:1011-1020.","ieee":"D. Cohen Steiner, H. Edelsbrunner, J. Harer, and D. Morozov, “Persistent homology for kernels, images, and cokernels,” presented at the SODA: Symposium on Discrete Algorithms, 2009, pp. 1011–1020.","mla":"Cohen Steiner, David, et al. <i>Persistent Homology for Kernels, Images, and Cokernels</i>. SIAM, 2009, pp. 1011–20.","short":"D. Cohen Steiner, H. Edelsbrunner, J. Harer, D. Morozov, in:, SIAM, 2009, pp. 1011–1020.","ista":"Cohen Steiner D, Edelsbrunner H, Harer J, Morozov D. 2009. Persistent homology for kernels, images, and cokernels. SODA: Symposium on Discrete Algorithms, 1011–1020.","chicago":"Cohen Steiner, David, Herbert Edelsbrunner, John Harer, and Dmitriy Morozov. “Persistent Homology for Kernels, Images, and Cokernels,” 1011–20. SIAM, 2009.","apa":"Cohen Steiner, D., Edelsbrunner, H., Harer, J., &#38; Morozov, D. (2009). Persistent homology for kernels, images, and cokernels (pp. 1011–1020). Presented at the SODA: Symposium on Discrete Algorithms, SIAM."},"date_created":"2018-12-11T12:06:10Z","_id":"3967","publication_status":"published","day":"01","extern":1}