Floer Homology Groups in Yang-Mills Theory

by S. K. Donaldson

Overview

This monograph gives a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The material contained here was developed with specific applications in mind. However, it has now become clear that the techniques used are important for many current areas of research. An important example would be symplectic theory and gluing problems for self-dual metrics and other metrics with special holonomy. The author writes with the big picture constantly in mind. As well as a review of the current state of knowledge, there are sections on the likely direction of future research. Included in this are connections between Floer groups and the celebrated Seiberg-Witten invariants. The results described in this volume form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution.

Product Details

ISBN-13:	9780521808033
Publisher:	Cambridge University Press
Publication date:	01/10/2002
Series:	Cambridge Tracts in Mathematics , #147
Edition description:	New Edition
Pages:	246
Product dimensions:	6.65(w) x 8.90(h) x 0.71(d)

Table of Contents

1. Introduction; 2. Basic material; 3. Linear analysis; 4. Gauge theory and tubular ends; 5. The Floer homology groups; 6. Floer homology and 4-manifold invariants; 7. Reducible connections and cup products; 8. Further directions.

Editorial Reviews

"This book gives a thorough and extensive treatment...this text is a wonderfully written exposition of Floer homology which no mathematics library should be without." Mathematical Reviews

From the Publisher

In a relatively concise but comprehensive treatment, this monograph addresses one of the key developments in differential geometry in the past 20 years. The concept of Floer homology groups has advanced the areas of low-dimensional topology and symplectic geometry, and is relevant to quantum field theory. The first half of the text develops Floer's construction in the context of gauge theory over 3- and 4- dimensional manifolds. The second half pursues other technical aspects of the theory and looks ahead to further research (e.g., on modular forms). Includes 51 references. Annotation c. Book News, Inc., Portland, OR (booknews.com)