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math.AT2025
Filtered cospans and interlevel persistence with boundary conditions
Michael Usher
We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respec…
math.AT2023
Abstract interlevel persistence for Morse-Novikov and Floer theory
Michael Usher
We develop a general algebraic framework involving "Poincaré--Novikov structures" and "filtered matched pairs" to provide an abstract approach to the barcodes associated to the hom…