The Structure of Morphisms in Persistent Homology, I. Functorial Dualities

12/23/2020
by   Ulrich Bauer, et al.
0

We prove duality results for absolute and relative versions of persistent (co)homology, generalizing previous results in terms of barcodes. Due to their naturality, we can apply these results to morphisms in persistent homology that are induced by morphisms between filtrations. This lays the groundwork for the efficient computation of barcodes for images, kernels, and cokernels of such morphisms.

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