Abstract
This paper studies the basic K -theoretic properties of a triangulated persistence category (TPC). This notion was introduced in the preprint by Biran, Cornea, and Zhang (2024) and it is a type of category that can be viewed as a refinement of a triangulated category in the sense that the morphisms sets of a TPC are persistence modules. We calculate the K -groups in some basic examples and discuss an application to Fukaya categories and to the topology of exact Lagrangian submanifolds.
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