Persistent homology for kernels, images, and cokernels
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, Journal Article
Cohen-Steiner, D; Edelsbrunner, H; Harer, J; Morozov, D
Published in: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
January 1, 2009
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. Copyright © by SIAM.
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Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
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Publication Date
January 1, 2009
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1011 / 1020
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Cohen-Steiner, D., Edelsbrunner, H., Harer, J., & Morozov, D. (2009). Persistent homology for kernels, images, and cokernels. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 1011–1020. https://doi.org/10.1137/1.9781611973068.110
Cohen-Steiner, D., H. Edelsbrunner, J. Harer, and D. Morozov. “Persistent homology for kernels, images, and cokernels.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, January 1, 2009, 1011–20. https://doi.org/10.1137/1.9781611973068.110.
Cohen-Steiner D, Edelsbrunner H, Harer J, Morozov D. Persistent homology for kernels, images, and cokernels. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. 2009 Jan 1;1011–20.
Cohen-Steiner, D., et al. “Persistent homology for kernels, images, and cokernels.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Jan. 2009, pp. 1011–20. Scopus, doi:10.1137/1.9781611973068.110.
Cohen-Steiner D, Edelsbrunner H, Harer J, Morozov D. Persistent homology for kernels, images, and cokernels. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. 2009 Jan 1;1011–1020.
Published In
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
DOI
Publication Date
January 1, 2009
Start / End Page
1011 / 1020