The Breadth of Symplectic and Poisson Geometry Festschrift in Honor
One of the world’s foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields. Written in his honor, the invited papers in this volume reflect the active and vibrant re
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Series Editors Hyman Bass Joseph Oesterl´e Alan Weinstein
The Breadth of Symplectic and Poisson Geometry Festschrift in Honor of Alan Weinstein
Jerrold E. Marsden Tudor S. Ratiu Editors
Birkh¨auser Boston • Basel • Berlin
Jerrold E. Marsden California Institute of Technology Department of Engineering and Applied Science Control and Dynamical Systems Pasadena, CA 91125 U.S.A.
Tudor S. Ratiu Ecole Polytechnique F´ed´erale de Lausanne D´epartement de Math´ematiques CH-1015 Lausanne Switzerland
AMS Subject Classifications: 53Dxx, 17Bxx, 22Exx, 53Dxx, 81Sxx Library of Congress Cataloging-in-Publication Data The breadth of symplectic and Poisson geometry : festschrift in honor of Alan Weinstein / Jerrold E. Marsden, Tudor S. Ratiu, editors. p. cm. – (Progress in mathematics ; v. 232) Includes bibliographical references and index. ISBN 0-8176-3565-3 (acid-free paper) 1. Symplectic geometry. 2. Geometric quantization. 3. Poisson manifolds. I. Weinstein, Alan, 1943- II. Marsden, Jerrold E. III. Ratiu, Tudor S. IV. Progress in mathematics (Boston, Mass.); v. 232. QA665.B74 2004 516.3’.6-dc22
ISBN 0-8176-3565-3
2004046202
Printed on acid-free paper.
c 2005 Birkh¨auser Boston
All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkh¨auser Boston, c/o Springer Science+Business Media Inc., Rights and Permissions, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 987654321 www.birkhauser.com
SPIN 10958261
(JLS/HP)
Margo, Alan, and Asha in Paris at the lovely Fontaine des Quatre Parties du Monde.
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Academic genealogy of Alan Weinstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii About Alan Weinstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Students of Alan Weinstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Alan Weinstein’s publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi Dirac structures, momentum maps, and quasi-Poisson manifolds Henrique Bursztyn, Marius Crainic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Construction of Ricci-type connections by reduction and induction Michel Cahen, Simone Gutt, Lorenz Schwachhöfer . . . . . . . . . . . . . . .
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