An Introduction to Differential Manifolds
This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic different
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S C I E N C E S
An Introduction to Differential Manifolds
Jacques Lafontaine
An Introduction to Differential Manifolds
Grenoble Sciences The aim of Grenoble Sciences is twofold: to produce works corresponding to a clearly defined project, without the constraints of trends nor curriculum, to ensure the utmost scientific and pedagogic quality of the selected works: each project is selected by Grenoble Sciences with the help of anonymous referees. In order to optimize the work, the authors interact for a year (on average) with the members of a reading committee, whose names figure in the front pages of the work, which is then co-published with the most suitable publishing partner. Contact Tel.: (33) 4 76 51 46 95 E-mail: [email protected] Website: https://grenoble-sciences.ujf-grenoble.fr Scientific Director of Grenoble Sciences Jean Bornarel, Emeritus Professor at the Joseph Fourier University, Grenoble, France Grenoble Sciences is a department of the Joseph Fourier University supported by the ministère de l’Enseignement supérieur et de la Recherche and the région Rhône-Alpes. An Introduction to Differential Manifolds is a translation of the original book Introduction aux variétés différentielles (2nd ed.) by Jacques Lafontaine, EDP Sciences, Grenoble Sciences Series, 2010, ISBN 978 2 7598 0572 3. The reading committee of the French version included the following members: Pierre Averbuch, Emeritus CNRS Senior Researcher, Grenoble Pierre Bérard, Professor, Joseph Fourier University, Grenoble I Gaël Meigniez, Professor, Bretagne-Sud University Jean-Yves Mérindol, Professor, President of Sorbonne Paris Cité Translation from original French version performed by Éric Bahuaud; excerpt from le Livre de mon ami by Anatole France translated by Jonathan Upjohn; typesetting: ARCHITEX; figures: Sylvie Bordage; cover illustration: Alice Giraud, after Klein bottle by Thomas Banchoff and Jeff Beall (Brown University), The “figure 8” immersion of the Klein bottle by Fropuff and Inductiveload (KleinBottle-Figure8-01.png, 2007, Wikimedia Commons) and elements provided by the author.
Jacques Lafontaine
An Introduction to Differential Manifolds
Jacques Lafontaine Département de Mathématiques Université Montpellier 2 Montpellier, France
Based on a translation from the French language edition: ‘Introduction aux variétés différentielles’ (2ème édition) by Jacques Lafontaine Copyright © EDP Sciences, 2010 All Rights Reserved ISBN 978-3-319-20734-6 ISBN 978-3-319-20735-3 (eBook) DOI 10.1007/978-3-319-20735-3 Library of Congress Control Number: 2015946989 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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, electro
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