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Persistence K-theory

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arxiv 2305.01370 v2 pith:IWE3SAFN submitted 2023-05-02 math.SG math.AT

Paul Biran , Octav Cornea , Jun Zhang This is my paper · ORCID
classification math.SGmath.AT
keywords persistencecategorysomearxivbasiccategoriesfukayatriangulated
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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.

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Cited by 1 Pith paper

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  1. Filtered Topology and Persistence in Stable Homotopy

    math.AT 2025-05 reject novelty 7.0 of 10

    A persistence Spanier-Whitehead category of filtered CW complexes is defined, proven to be a triangulated persistence category, and its K-group is shown to be isomorphic to the Novikov polynomial ring via the weighted...

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