An Introduction to Manifolds (Second edition)

For other titles in this series, go Board(North America):S. Ribet An Introduction to ManifoldsLoring W. TuSecond Edition c Editorial board:Sheldon Axler, San Francisco State UniversityVincenzo Capasso, Universit degli Studi di MilanoCarles Casacuberta, Universitat de BarcelonaAngus MacIntyre, Queen Mary, University of LondonKenneth Ribet, University of California, BerkeleyClaude Sabbah, CNRS, cole PolytechniqueEndre S li, University of OxfordWojbor Woyczy nski, Case Western Reserve UniversityLoring W. TuDepartment of MathematicsTufts UniversityMedford, MA 978-1-4419-7399-3 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connectionAll rights reserved. This work may not be translated or copied in whole or in part without the writtenwith any form of information storage and retrieval, electronic adaptation, computer software, or by similaror dissimilar methodology now known or hereafter developed is use in this publication of trade names, trademarks, service marks, and similar terms, even if they arenot identified as such, is not to be taken as an expression of opinion as to whether or not they are subjectto proprietary on acid-free paperSpringer is part of Springer Science+Business Media ( )e-IS BN 978-1-4419-7400-6 DOI of Congress Control Number: Mathematics Subject Classification (2010): 58-01, 58 Axx, 58A05, 58A1

An Introduction to Manifolds ... With so many excellent books on manifolds on the market, any author who un-dertakesto write anotherowes to the public, if not to himself, a good rationale. First and foremost is my desire to write a readable but rigorous introduction that gets the

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