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57 DON (Browse shelf) Available 01770-01

This book successfully gives a self-contained and comprehensive treatment of the applications of Yang-Mills theory to 4-manifold topology that were pioneered and developed by Donaldson and brings together the internal developments of Yang-Mills theory within the framework of contemporary differential and algebraic geometry. Most of the results that appear in this book have appeared in research papers. However, the proofs that are presented are different, simplified, and crafted so as to streamline the exposition. This book is a model at filling the gap between general textbooks and research papers.
The prerequisites for this book are somewhat daunting: sound one-year graduate courses in topology, differential geometry, algebraic geometry, and global analysis. There is some help: the appendix assembles the many facts from analysis that are used throughout the book. Notes at the end of each chapter contain ample references to enable the reader to track down what is needed and provide informative commentary on the material covered. The material presented, although developed to dramatically enhance the understanding of smooth 4-manifolds, encompasses several diverse areas of mathematics (MathSciNet).

Bibliogr. p. [427]-436. Index

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