Monopoles and Three-Manifolds [Hardcover]

A comprehensive treatment of Floer homology, based on the SeibergWitten equations, first published in 2007.This 2007 book provides a comprehensive treatment of Floer homology, based on the SeibergWitten equations. Suitable for beginning graduate students and researchers in the field, this book provides a full discussion of a central part of the study of the topology of manifolds.This 2007 book provides a comprehensive treatment of Floer homology, based on the SeibergWitten equations. Suitable for beginning graduate students and researchers in the field, this book provides a full discussion of a central part of the study of the topology of manifolds.Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology. This book provides a comprehensive treatment of Floer homology, based on the SeibergWitten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the SeibergWitten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides the first full discussion of a central part of the study of the topology of manifolds since the mid 1990s.Preface; 1. Outlines; 2. The SeibergWitten equations and compactness; 3. Hilbert manifolds and perturbations; 4. Moduli spaces and transversality; 5. Compactness and gluing; 6. Floer homology; 7. Cobordisms and invariance; 8. Non-exact perturbations; 9. Calculations; 10. Further developments; References; Glossary of notation; Index.'& there are mathematics books that are classics; these are books that tell a particular story in the right way.ls.