Smooth Four-Manifolds and Complex Surfaces

ISBN-13: 9783540570585 / Angielski / Twarda / 1994 / 522 str.

Robert Friedman; John W. Morgan

Opis

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.

Spis treści

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.