Persistence theory
Subtitle: from quiver representations to data analysis
By: Steve Y. Oudot
Series: Mathematical surveys and monographs -- volume 209
Publisher: American Mathematical Society
Published: 2015
Place of publication: Providence, Rhode Island
Language: eng
Number of pages: 218
ISBN-13: 9781470425456
Subjects: Associative rings and algebras -- Representation theory of rings and algebras -- Representations of quivers and partially ordered sets; Homology theory; Algebraic topology -- Applied homological algebra and category theory -- Simplicial sets and complexes; Statistics -- Data analysis; Computer science -- Computing methodologies and applications -- Computer graphics; computational geometry; Algebraic topology
Description: "Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organizaed into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis"--Back cover.
Notes: Includes bibliographical references and index.