Zig-Zag Modules: Cosheaves and K-Theory

10/09/2021
by   Ryan E. Grady, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset