The Structure and Stability of Persistence Modules

• Main Authors: Chazal, Frédéric (Author), de Silva, Vin (Author), Glisse, Marc (Author), Oudot, Steve (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: SpringerBriefs in Mathematics,
• Subjects: Mathematics.; Algebra.; Computer science > Mathematics.; Computer mathematics.; Algebraic topology.; Algebraic Topology.; Mathematical Applications in Computer Science.
• Physical Description: X, 120 p. 17 illus., 15 illus. in color. online resource.
• ISBN: 9783319425450
• ISSN: 2191-8198

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.