Persistence $K$-theory

Paul Biran; Octav Cornea; Jun Zhang

doi:10.4171/qt/222

JournalsqtVol. 17, No. 4pp. 799–875

Persistence $K$ -theory

Paul Biran
ETH-Zürich, Switzerland
Octav Cornea
University of Montreal, Canada
Jun Zhang
University of Science and Technology of China, Anhui, P. R. China

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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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Paul Biran, Octav Cornea, Jun Zhang, Persistence $K$ -theory. Quantum Topol. 17 (2026), no. 4, pp. 799–875

DOI 10.4171/QT/222