Topology, Geometry and Gauge fields Foundations
This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author’s point of view is that the rekindled interest that mathematics and physics have shown in each
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25 Editors
J.E. Marsden L. Sirovich S.S. Antman Advisors
G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton
For other volumes published in this series, go to www.springer.com/series/1214
Gregory L. Naber
Topology, Geometry, and Gauge Fields Foundations Second Edition
With 65 Illustrations
123
Gregory L. Naber Department of Mathematics Drexel University Philadelphia, PA 19104-2875 USA
Series Editors J.E. Marsden Control and Dynamical Systems, 107–81 California Institute of Technology Pasadena, CA 91125 USA [email protected] L. Sirovich Laboratory of Applied Mathematics Mt. Sinai School of Medicine Box 1012 New York City, NY 10029 USA [email protected]
S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA [email protected]
ISSN 0939-2475 ISBN 978-1-4419-7253-8 e-ISBN 978-1-4419-7254-5 DOI 10.1007/978-1-4419-7254-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010936347 Mathematics Subject Classification (2010): 53-01, 53B21, 55-01, 70S15 c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 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 on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
This book is dedicated, with love and gratitude, to the memories of my mom and dad, Marguerite and Bernard Naber. Poor payment for so great a debt.
Series Preface
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM ). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses
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