K-Theory of Multi-parameter Persistence Modules: Additivity

06/10/2023

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by   Ryan E. Grady, et al.

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Persistence modules stratify their underlying parameter space, a quality that make persistence modules amenable to study via invariants of stratified spaces. In this article, we extend a result previously known only for one-parameter persistence modules to grid multi-parameter persistence modules. Namely, we show the K-theory of grid multi-parameter persistence modules is additive over strata. This is true for both standard monotone multi-parameter persistence as well as multi-parameter notions of zig-zag persistence. We compare our calculations for the specific group K_0 with the recent work of Botnan, Oppermann, and Oudot, highlighting and explaining the differences between our results through an explicit projection map between computed groups.