Holomorphic Curves in Low Dimensions From Symplectic Ruled Surfaces

This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three.The first half of the book focuses on McDuff's characterization of symplectic

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Chris Wendl

Holomorphic Curves in Low Dimensions From Symplectic Ruled Surfaces to Planar Contact Manifolds

Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Zurich Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg

2216

More information about this series at http://www.springer.com/series/304

Chris Wendl

Holomorphic Curves in Low Dimensions From Symplectic Ruled Surfaces to Planar Contact Manifolds

123

Chris Wendl Institut f: ur Mathematik Humboldt-Universit:at zu Berlin Berlin, Germany

ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-91369-8 ISBN 978-3-319-91371-1 (eBook) https://doi.org/10.1007/978-3-319-91371-1 Library of Congress Control Number: 2018943453 Mathematics Subject Classification (2010): 57R17, 32Q65 © Springer International Publishing AG, part of Springer Nature 2018 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Clara, whose entry into the world may have slightly delayed the completion of this book.

Preface

This book is an expanded version of a set of lecture notes for a minicourse I gave at IRMA Strasbourg in October 2012 as part of the Master Classes on Holomorphic Curves and Applications to Enumerative Geometry, Symplectic and Contact Topology. The focus of the minicourse was on certain specifically lowdimensional aspects of the theory of pseudoholomorphic curves, which lend a distinctive flavor to the study of symplectic a