Smooth Manifolds and Observables
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Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo
220
Editorial Board F.W. Gehring K.A. Ribet
Jet Nestruev
Smooth Manifolds and Observables
123
Editorial Board S. Axler Mathematics Department San Francisco State University San Francisco, CA 94132 USA [email protected]
F.W. Gehring Mathematics Department East Hall University of Michigan Ann Arbor, MI 48109 USA [email protected]
K.A. Ribet Mathematics Department University of California, Berekeley Berkeley, CA 94720-3840 USA [email protected]
Mathematics Subject Classification (2000): 58-01, 58Jxx, 55R05, 13Nxx, 8 Library of Congress Cataloging-in-Publication Data Nestruev, Jet. Smooth manifolds and observables / Jet Nestruev. p. cm.—(Graduate texts in mathematics ; 220) Includes bibliographical references and index. ISBN 0-387-95543-7 (alk. paper) 1. Manifolds (Mathematics) I. Title. II. Series. QA613 .N48 2002 516'.07—dc21 2002026664 ISBN 0-387-95543-7
Printed on acid-free paper.
© 2003 Springer-Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, 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. 9 8 7 6 5 4 3 2 1
SPIN 10885698
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Preface to the English Edition
The author is very pleased that his book, first published in Russian in 2000 by MCCME Publishers, is now appearing in English under the auspices of such a truly classical publishing house as Springer-Verlag. In this edition several pertinent remarks by the referees (to whom the author expresses his gratitude) were taken into account, and new exercises were added (mostly) to the first half of the book, thus achieving a better balance with the second half. Besides, some typos and minor errors, noticed in the Russian edition, were corrected. We are extremely grateful to all our readers who assisted us in this tiresome bug hunt. We are especially grateful to A. De Paris, I. S. Krasil’schik, and A. M. Verbovetski, who demonstrated their acute eyesight, truly of degli Lincei standards. The English translation was carried out by A. B. Sossinsky (Chapters 1–8), I. S. Krasil’schik (Chapter 9), and S. V. Duzhin (Chapters 10–11) and reduced to a common denominator by the first of them; A. M. Astashov prepare
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