arXiv:2012.12881 Abstract | arXiv Analytics

arXiv:2012.12881 [math.AT]Abstract References Reviews Resources

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

Published 2020-12-23Version 1

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.

Comments: 25 pages, 1 figure

Categories: math.AT, cs.CG

Subjects: 55N31, 55U10

Keywords: persistent homology, functorial dualities, duality results, efficient computation, naturality

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