Overview

This book applies the recent techniques of gauge theory to study the smooth classification of compact complex surfaces. The study is divided into four main areas: Classical complex surface theory, gauge theory and Donaldson invariants, deformations of holomorphic vector bundles, and explicit calculations for elliptic sur faces. The book represents a marriage of the techniques of algebraic geometry and 4-manifold topology and gives a detailed exposition of some of the main themes in this very active area of current research.

Full Product Details

Author:   Robert Friedman ,  John W. Morgan
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 1994
Volume:   27
Dimensions:   Width: 15.50cm , Height: 2.70cm , Length: 23.50cm
Weight:   0.807kg
ISBN:  

9783642081712

ISBN 10:   3642081711
Pages:   522
Publication Date:   05 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I. The Kodaira Classification of Surfaces.- II. The Topology of Elliptic Surfaces.- III. Definition of the Polynomial Invariants.- IV. Holomorphic Vector Bundles, Stability, and Gauge Theory.- V. Donaldson Polynomials of Algebraic Surfaces.- VI. Big Diffeomorphism Groups and Minimal Models.- VII. Donaldson Polynomials of Elliptic Surfaces.- References.- Index of Notation.

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