Smooth Four-Manifolds and Complex Surfaces

1994
ISBN: 978-3-540-57058-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 27, 522 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 2040 g

Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

With this book, appearing in Springer's prestigious series Ergebnisse der Mathematik, Friedman and Morgan give a comprehensive introduction to current research in the field of applications of gauge theory to complex surfaces. Their streamlined modern presentation of this very active area of mathematical research will be very welcome to researchers and graduate students alike. The study is divided into 4 main areas: - Classical complex surface theory; - gauge theory and Donaldson invariants; - deformations of holomorphic vector bundles; - explicit calculations for elliptic surfaces. The book very successfully bridges the two areas of 4-manifold topology and complex surface theory, thus unifying the classical theory of Barth/Peters/van de Ven (ERGEBNISSE 4) with gauge theory techniques described by Donaldson/Kronheimer.

Zielgruppe

Research

Autoren/Hrsg.

Morgan, John W.

Friedman, Robert

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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.