The geometry of four-manifolds / S. K. Donaldson and P. B. KronheimerType de document : MonographieCollection : Oxford mathematical monographsLangue : anglais.Pays : Etats Unis.Mention d'édition: Reprint 2001Éditeur : New York : Oxford University Press, 2001Description : 1 vol. (ix-440 p.) : ill. ; 24 cmISBN : 0198502699.ISSN : 0964-9174.Bibliographie : Bibliogr. p. -436. Index.Sujet MSC : 57K40, Manifolds and cell complexes - Low-dimensional topology in specific dimensions, General topology of 4-manifolds
57R57, Manifolds and cell complexes - Differential topology, Applications of global analysis to structures on manifolds
58D27, Global analysis, analysis on manifolds - Spaces and manifolds of mappings, Moduli problems for differential geometric structures
57R55, Manifolds and cell complexes, Differentiable structures in differential topology
58J10, Global analysis, analysis on manifolds - PDEs on manifolds; differential operators, Differential complexes; elliptic complexesEn-ligne : Zentralblatt | MathSciNet
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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. -436. Index