Persistence Modules
This chapter introduces the basic properties of persistence modules. These can be defined over any partially ordered set; we are primarily interested in persistence modules over the real line or over a finite subset of the real line. In the best cases, a
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Frédéric Chazal Vin de Silva Marc Glisse Steve Oudot
The Structure and Stability of Persistence Modules 123
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Frédéric Chazal Vin de Silva Marc Glisse Steve Oudot •
•
The Structure and Stability of Persistence Modules
123
Frédéric Chazal Inria Saclay – Île-de-France Palaiseau France
Marc Glisse Inria Saclay – Île-de-France Palaiseau France
Vin de Silva Pomona College Claremont, CA USA
Steve Oudot Inria Saclay – Île-de-France Palaiseau France
ISSN 2191-8198 SpringerBriefs in Mathematics ISBN 978-3-319-42543-6 DOI 10.1007/978-3-319-42545-0
ISSN 2191-8201
(electronic)
ISBN 978-3-319-42545-0
(eBook)
Library of Congress Control Number: 2016945105 Mathematics Subject Classification (2010): 55-02, 16G20 © The Author(s) 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Preface
Our intention, at the beginning, was to write a short paper resolving some technical issues in the theory of topological persistence. Specifically, we wished to present a clean easy-to-use framework for continuous-parameter persistence, building on the well-studied case of discrete-parameter persistence. Over a number of years, we gradually abandoned the idea of a short paper. It apparent
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