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• W2980036332 abstract "The classical Kunneth formula in algebraic topology describes the homology of a product space in terms of that of its factors. In this paper, we prove Kunneth-type theorems for the persistent homology of the categorical and tensor product of filtered spaces. That is, we describe the persistent homology of these product filtrations in terms of that of the filtered components. In addition to comparing the two products, we present two applications in the setting of Vietoris-Rips complexes: one towards more efficient algorithms for product metric spaces with the maximum metric, and the other recovering persistent homology calculations on the $n$-torus." @default.
• W2980036332 created "2019-10-18" @default.
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• W2980036332 date "2018-01-01" @default.
• W2980036332 modified "2023-10-01" @default.
• W2980036332 title "Kunneth formuale in persistent homology" @default.
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• W2980036332 doi "https://doi.org/10.14288/1.0377398" @default.
• W2980036332 hasPublicationYear "2018" @default.
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