Del 10 i serien New Mathematical Monographs

Monopoles and Three-Manifolds

Inbunden, Engelska, 2007

AvPeter Kronheimer,Tomasz Mrowka

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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 2007 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 a full discussion of a central part of the study of the topology of manifolds.

Produktinformation

Utgivningsdatum2007-12-20
Mått152 x 229 x 49 mm
Vikt1 350 g
FormatInbunden
SpråkEngelska
SerieNew Mathematical Monographs
Antal sidor810
FörlagCambridge University Press
ISBN9780521880220

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Topologi inom Naturvetenskap och teknik

Peter Kronheimer is William Caspar Graustein Professor in the Department of Mathematics at Harvard University. He is a Fellow of the Royal Society and has been awarded several distinguished prizes including the 2007 Oswald Veblen Prize. He is co-author, with S. K. Donaldson, of The Geometry of Four-Manifolds. His research interests are gauge theory, low-dimensional topology and geometry. Tomasz Mrowka is Professor of Mathematics at Massachusetts Institute of Technology. He holds the James and Marilyn Simons Professorship of Mathematics and is a Member of the American Academy of Arts and Sciences. He was a joint recipient (with Peter Kronheimer) of the 2007 Oswald Veblen Prize. His research interests are low-dimensional topology, partial differential equations and mathematical physics.

'… there are mathematics books that are classics; these are books that tell a particular story in the right way. As such, they will never go out of date and never be bettered. Kronheimer and Mrowka's book is almost surely such a book. If you want to learn about Floer homology in the Seiberg–Witten context, you will do no better than to read Kronheimer and Mrowka's masterpiece Monopoles and Three-Manifolds.' Clifford Henry Taubes, Bulletin of the American Mathematical Society