Zig-Zag Modules: Cosheaves and K-Theory
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Persistence modules have a natural home in the setting of stratified spaces and constructible cosheaves. In this article, we first give explicit constructible cosheaves for common data-motivated persistence modules, namely, for modules that arise from zig-zag filtrations (including monotone filtrations), and for augmented persistence modules (which encode the data of instantaneous events). We then identify an equivalence of categories between a particular notion of zig-zag modules and the combinatorial entrance path category on stratified ℝ. Finally, we compute the algebraic K-theory of generalized zig-zag modules and describe connections to both Euler curves and K_0 of the monoid of persistence diagrams as described by Bubenik and Elchesen.
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