Persistence K-theory

This paper studies the basic K-theoretic properties of a triangulated persistence category (TPC). This notion was introduced in our earlier papers on triangulation, persistence, and Fukaya categories (arXiv:2304.01785 and arXiv:2104.12258) 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. The second version contains some changes in the exposition and the correction of some minor imprecisions.