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Smooth four-manifolds and complex surfaces

Author: Robert Friedman; John Morgan
Publisher: Berlin ; New York : Springer-Verlag, 1994.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Bd. 27.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver.

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Additional Physical Format: Online version:
Friedman, Robert, 1955-
Smooth four-manifolds and complex surfaces.
Berlin ; New York : Springer-Verlag, 1994
(OCoLC)824538689
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Robert Friedman; John Morgan
ISBN: 3540570586 9783540570585 0387570586 9780387570587
OCLC Number: 28962004
Description: x, 520 pages : illustrations ; 24 cm.
Contents: Ch. I. The Kodaira Classification of Surfaces. 1.1. An Overview of the Enriques-Kodaira Classifications. 1.2. Homotopy Type and Deformation Type for Nonelliptic Surfaces. 1.3. First Properties of Elliptic Surfaces. 1.4. Elliptic Surfaces with a Section. 1.5. Elliptic Surfaces with No Multiple Fibers. 1.6. Logarithmic Transforms and Multiple Fibers. 1.7. Deformation Equivalence for Elliptic Surfaces --
Ch. II. The Topology of Elliptic Surfaces. 2.1. General Results. 2.2. The Case of Positive Euler Number. 2.3. Monodromy of Elliptic Surfaces over P[superscript 1]. 2.4. Appendix to Section 3. 2.5. Embedded 2-Spheres of Square -2 in Rational Elliptic Surfaces and the Associated Reflection Group. 2.6. Embedded 2-Spheres of Square -2 in Elliptic Surfaces and the Reflection Groups They Generate. 2.7. Elliptic Surfaces with Euler Number Zero --
Ch. III. Definition of the Polynomial Invariants. 3.1. The Space of Connections. 3.2. The Moduli Space of Anti-self-dual Connections. 3.3. The Completion of M(P, g). 3.4. The Local Stratification and Its Local Structure. 3.5. The Thickened Completion X[delta](P, g) of the Moduli Space and Its Fundamental Class. 3.6. Extension of the [mu]-Map over X[delta](P, g). 3.7. The Stable Donaldson Polynomial Invariants. 3.8. The Full Donaldson Polynomial Invariant --
Ch. IV. Holomorphic Vector Bundles, Stability, and Gauge Theory. 4.1. The Moduli Space of Holomorphic Structures on a Vector Bundle. 4.2. The Moduli Functor. 4.3. Kahler Differential Geometry and ASD Connections. 4.4. Some Global Properties of the Moduli Space --
Ch. V. Donaldson Polynomials of Algebraic Surfaces. 5.1. Computing Donaldson Polynomials of Algebraic Surfaces. 5.2. Nonvanishing of the Polynomial Invariants. 5.3. Appendix: A Comparison of Determinant Line Bundles --
Ch. VI. Big Diffeomorphism Groups and Minimal Models. 6.1. Notation and Conventions. 6.2. Definitions, Examples, and First Properties. 6.3. Generalized Donaldson Polynomial Invariants and Blow Ups. 6.4. Minimal Models for Smooth 4-Manifolds. 6.5. More General Connected Sums. 6.6. Appendix --
Ch. VII. Donaldson Polynomials of Elliptic Surfaces. 7.1. Description of the Moduli Space of Stable Bundles. 7.2. Computation of the Leading Coefficient. 7.3. Some Consequences and Conjectures.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Bd. 27.
Responsibility: John Friedman, John W. Morgan.
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