Smooth Four-Manifolds and Complex Surfaces
In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological struc
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Editorial Board
E. Bombieri, Princeton S. Feferman, Stanford M. Gromov, Bures-sur-Yvette H.W Lenstra, Jr., Berkeley P.-L. Lions, Paris R. Remmert (Managing Editor), MUnster w. Schmid, Cambridge, Mass. J-P. Serre, Paris J.Tits, Paris
Robert Friedman John W. Morgan
Smooth Four-Manifolds and Complex
Surfaces With 17 Figures
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Springer-Verlag Berlin Heidelberg GmbH
Robert Friedman John W Morgan Department of Mathematics Columbia University New York, NY 10027, USA
Mathematics Subject Classification (1991): 14Jl5, 14127, 14F05, 32Gl3, 57R55, 58D27
ISBN 978-3-642-08171-2
Library of Congress Cataloging-in-Publication Data. Friedman, Robert, 1955- Smooth four-manifolds and complex surfacesl Robert Friedman, John W. Morgan. p. cm. - (Ergebnisse der Mathematik und ihrer Grenzgebiete; 3. Folge, Bd. 27) Includes bibliographical references and indexes. ISBN 978-3-642-08171-2 ISBN 978-3-662-03028-8 (eBook) DOI 10.1007/978-3-662-03028-8 1. Four-manifolds (Topology) 2. Surfaces, Algebraic. I. Morgan, John W., 1946- . II. Title. III. Series. QA613.2.F76 1994 514'.3 - dc20 93-34949 CIP This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, 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 current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1994 Originally published by Springer-Verlag Berlin Heidelberg New York in 1994 Softcover reprint of the hardcover I st edition 1994
Typesetting: Camera-ready copy produced from the authors' input file using a Springer TEX macro package 4113140 - 5 4 3 2 I 0 - Printed on acid-free paper
Contents
Introduction ..........................................................
1
Chapter 1. The Kodaira Classification of Surfaces .....................
14
1.1 An Overview of the Enriques-Kodaira Classification .............. 1.1.1 Preliminaries.............................................. 1.1.2 An Outline of the Classification... . . . . ... . . .. . . . . ... . . . . . . . 1.1.3 The Case K, = -00 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 The Case K, = 0 ............................................ 1.1.5 The Case K, = 1 ............................................ 1.1.6 The Case K, = 2 ............................................ 1.1.7 A Proof of Theorem 1.12 .................................. 1.2 Homotopy Type and Deformation Type for Nonelliptic Surfaces .. 1.2.1 The Case of Ruled Surfaces................................ 1.2.2 Surfaces of Kodaira Dimension 0 ........................... 1.2.3 Surfaces of General Type.................................. 1.3 First Properties of
