Monopoles and Three-Manifolds

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Originating with Andreas Floer in the 1980s, Floer homology provides an invariant of three-dimensional manifolds and four-dimensional cobordisms between them. It 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 Seiberg-Witten equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg-Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer gr...