Monopoles and Three-Manifolds
Monopoles and Three-Manifolds by Peter Kronheimer, published by Cambridge University Press on November 25, 2010, is an illustrated edition comprising 808 pages. This book offers a comprehensive treatment of Floer homology, a mathematical tool that has been instrumental in addressing significant problems in three- and four-dimensional geometry and topology. It begins with an overview of results and progresses to the analytic properties of the Seiberg-Witten monopole equations, requiring only a basic understanding of differential geometry and analysis.
Readers will find a detailed exploration of the Floer groups of general three-manifolds, along with an in-depth study of their properties. The book also includes two final chapters dedicated to the calculation of Floer groups and their applications in topology. Aimed at beginning graduate students and researchers, this work represents a thorough discussion of a central aspect of manifold topology, reflecting developments in the field since the mid-1990s.
Official synopsis Publisher
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 Seiberg-Witten monopole 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 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.
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