EDITORIAL COMMITTEE Dan Abramovich Daniel S. Freed Rafe Mazzeo (Chair) Gigliola Staffilani 2010 Mathematics Subject Classification. Primary 22D05, 22E05, 22E15, 11B30, 20F65. For additional information and updates on this book, visit www.ams.org/bookpages/gsm-153 Library of Congress Cataloging-in-Publication Data Tao, Terence, 1975– Hilbert’s fifth problem and related topics / Terence Tao. pages cm. (Graduate studies in mathematics volume 153) Includes bibliographical references and index. ISBN 978-1-4704-1564-8 (alk. paper) 1. Hilbert, David, 1862–1943. 2. Lie groups. 3. Lie algebras. Characteristic functions. I. Title. QA387.T36 2014 512 .482–dc23 2014009022 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA. Requests can also be made by e-mail to reprint-permission@ams.org. c 2014 by Terence Tao. All right reserved. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ 10 9 8 7 6 5 4 3 2 1 19 18 17 16 15 14
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