Introduction to Symplectic Geometry
This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters: Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplect
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Introduction to Symplectic Geometry
Introduction to Symplectic Geometry
Jean-Louis Koszul Yi Ming Zou •
Introduction to Symplectic Geometry
123
Jean-Louis Koszul Institut Fourier Université Grenoble Alpes Gières, Grenoble, Isère, France
Yi Ming Zou Department of Mathematical Sciences University of Wisconsin-Milwaukee Milwaukee, WI, USA
ISBN 978-981-13-3986-8 ISBN 978-981-13-3987-5 https://doi.org/10.1007/978-981-13-3987-5
(eBook)
Jointly published with Science Press, Beijing, China The print edition is not for sale in China Mainland. Customers from China Mainland please order the print book from: Science Press Library of Congress Control Number: 2018965909 Mathematics Subject Classification (2010): 53Dxx © Springer Nature Singapore Pte Ltd. and Science Press 2019 This work is subject to copyright. All rights are reserved by the Publishers, 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 publishers, 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 publishers 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. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Foreword 1. About This Book
En effet, Barbaresco m’a dit qu’il était curieux de voir le texte qui a été publié d’après un cours sur la géométrie symplectique que j’ai donné à Tianjin, il y a bien longtemps. Je n’ai rien pu lui procurer d’autre que le petit fascicule rédigé en chinois par un assistant de Nankai. Je ne sais pas ce qu’il vaut. De toutes façons, il n’y avait pas beaucoup de choses originales dans ce que j’ai raconté. Indeed, Barbaresco told me that he was curious to see the text that was published according to a course on symplectic geometry that I gave in Tianjin, long time ago. I could not give anything else but the little notebook written in Chinese by a Nankai assistant. I do not know whether it was worthful. In any case, there were no too many original things in what I was speaking about. J.-L. Koszul, 02/02/2017. Above is an e
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