The Structure and Stability of Persistence Modules

This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations.
Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.

Provides a comprehensive treatment of 1-parameter persistence modules Presents new tools for studying persistence modules in wide generality Introduces the measure-theory approach to persistence diagrams Offers a definitive treatment of the stability theorem

Inhalt
Introduction.- Persistence Modules.- Rectangle Measures.- Interleaving.- The Isometry Theorem.- Variations.- References.- Index.