Classical Manifolds
This article contains a variety of information (mainly topological, but also geometric and analytic) about classical manifolds, such as spheres, Stiefel and Grassmann manifolds, Lie groups, and lens spaces (a fuller list of the manifolds considered can be
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Editor-in-Chief: R.V. Gamkrelidze
Springer-V erlag Berlin Heide1berg GmbH
S. P. N ovikov V. A. Rokhlin (Eds.)
Topology II Homotopy and Homology. Classical Manifolds
Springer
Consulting Editors of the Series: A.A. Agrachev, A.A. Gonchar, E.F. Mishchenko, N. M. Ostianu, V. P. Sakharova, A. B. Zhishchenko
Title of the Russian original edition: ltogi nauki i tekhniki, Sovremennye problemy matematiki, Fundamental'nye napravleniya, VoI. 24, Topologiya-2, and Part II of VoI. 12, Topologiya-l Publisher VINITl, Moscow
Mathematics Subject Classification (2000): 55Pxx, 55Nxx, 57Nxx
ISSN 0938-0396 ISBN 978-3-642-08084-5 ISBN 978-3-662-10581-8 (eBook) DOI 10.1007/978-3-662-10581-8 This work is subject to copyright. Ali rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of iIlustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its curreot version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are !iabte for prosecution under the German Copyright Law.
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© Springer-Verlag Berlin Heidelberg 2004
Originally published by Sprioger-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover 1SI edition 2004 Part 1 and II typeset by Kurt Mattes, Heidelberg. Part III typeset by Aseo Trade Typesetting Ltd., Hong Kong 46/3142 - 543210 Prioted 00 acid-free paper
List of Editors, Authors and Translator Editor-in-Chiej R.V. Gamkrelidze, Russian Academy of Sciences, Steklov Mathematical Institute, ul. Gubkina 8, 117966 Moscow; Institute for Scientific Infonnation (VINITI), ul. Usievicha 20a, 125219 Moscow, Russia, e-mail: [email protected]
Consulting Editors S. P. Novikov, Department of Mathematics, Institute for Physical Sciences and Technology, University of Maryland at College Park, College Park, MD 20742-2431, USA, e-mail: [email protected] V. A. Rokhlint
Authors D. B. Fuchs, Department of Mathematics, University of California, Davis, CA 95616-8633, USA, e-mail: [email protected] O. Ya. Viro, Department of Mathematics, Uppsala University, P.O. Box 480, 75106 Uppsala, Sweden, e-mail: [email protected]
Translator C. 1. Shaddock, 39 Drummond Place, Edinburgh EH3 6NR, United Kingdom
Contents
I. Introduction to Homotopy Theory O. Ya. Vira, D. B. Fuchs
1 II. Homology and Cohomology O. Ya. Viro, D. B. Fuchs 95 III. Classical Manifolds D. B. Fuchs 197 Index 253
Preface *
Aigebraic topology, which went through a period of intense development from the forties to the sixties ofthe last century, has now reached a comparatively stable state. A body of concepts and facts of general mathematical interest has been clearly demarcated, and at the same time the area of applications of topology has been significantly widened to include theoretical phy
