The Structure of Morphisms in Persistent Homology, I. Functorial Dualities
share
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.
READ FULL TEXT