TY  - BOOK
AU  - Chazal,Frédéric
AU  - de Silva,Vin
AU  - Glisse,Marc
AU  - Oudot,Steve
ED  - SpringerLink (Online service)
TI  - The Structure and Stability of Persistence Modules
T2  - SpringerBriefs in Mathematics,
SN  - 9783319425450
AV  - QA612-612.8 
U1  - 514.2 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Algebraic topology
KW  - Algebra
KW  - Algebraic Topology
KW  - Mathematical Applications in Computer Science
N1  - Introduction -- Persistence Modules -- Rectangle Measures -- Interleaving -- The Isometry Theorem -- Variations -- References -- Index
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-42545-0
ER  -