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Inverse problems in topological persistence. (English) Zbl 1447.55006
Baas, Nils (ed.) et al., Topological data analysis. Proceedings of the Abel symposium 2018, Geiranger, Norway, June 4–8, 2018. Cham: Springer. Abel Symp. 15, 405-433 (2020).
Summary: In this survey, we review the literature on inverse problems in topological persistence theory. The first half of the survey is concerned with the question of surjectivity, i.e. the existence of right inverses, and the second half focuses on injectivity, i.e. left inverses. Throughout, we highlight the tools and theorems that underlie these advances, and direct the reader’s attention to open problems, both theoretical and applied.
For the entire collection see [Zbl 1448.62008].
55N31 Persistent homology and applications, topological data analysis
55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology
68T09 Computational aspects of data analysis and big data
62R07 Statistical aspects of big data and data science
Full Text: DOI
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