Smooth Manifolds
This concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry; as space-times in general relativity;
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Claudio Gorodski
Smooth Manifolds
Compact Textbooks in Mathematics
Compact Textbooks in Mathematics This textbook series presents concise introductions to current topics in mathematics and mainly addresses advanced undergraduates and master students. The concept is to offer small books covering subject matter equivalent to 2- or 3-hour lectures or seminars which are also suitable for self-study. The books provide students and teachers with new perspectives and novel approaches. They may feature examples and exercises to illustrate key concepts and applications of the theoretical contents. The series also includes textbooks specifically speaking to the needs of students from other disciplines such as physics, computer science, engineering, life sciences, finance. • •
compact: small books presenting the relevant knowledge learning made easy: examples and exercises illustrate the application of the contents • useful for lecturers: each title can serve as basis and guideline for a semester course/lecture/seminar of 2–3 hours per week.
More information about this series at http://www.springer.com/series/ 11225
Claudio Gorodski
Smooth Manifolds
Claudio Gorodski Institute of Mathematics and Statistics University of São Paulo São Paulo, Brazil
ISSN 2296-4568 ISSN 2296-455X (electronic) Compact Textbooks in Mathematics ISBN 978-3-030-49774-3 ISBN 978-3-030-49775-0 (eBook) https://doi.org/10.1007/978-3-030-49775-0 Mathematics Subject Classification (2020): 58-01, 57-01, 22-01, 57RXX, 53A45 © Springer Nature Switzerland AG 2020 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, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com, by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
TO MY SON, DAVID
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Preface The concept of smooth manifold is ub
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