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Loop Spaces, Characteristic Classes and Geometric Quantization (Modern Birkhäuser Classics) - Softcover
Synopsis
This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger-Chern-Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac's quantization of the electrical charge.
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From the Back Cover
This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics.
Various developments in mathematical physics (e.g., in knot theory, gauge theory, and topological quantum field theory) have led mathematicians and physicists to search for new geometric structures on manifolds and to seek a synthesis of ideas from geometry, topology and category theory. In this spirit, this book develops the differential geometry associated to the topology and obstruction theory of certain fiber bundles (more precisely, associated to grebes). The theory is a 3-dimensional analog of the familiar Kostant--Weil theory of line bundles. In particular the curvature now becomes a 3-form.
Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, Cheeger--Chern--Simons secondary characteristics classes, and group cohomology. Finally, the last chapter deals with the Dirac monopole and Dirac’s quantization of the electrical charge.
The book will be of interest to topologists, geometers, Lie theorists and mathematical physicists, as well as to operator algebraists. It is written for graduate students and researchers, and will be an excellent textbook. It has a self-contained introduction to the theory of sheaves and their cohomology, line bundles and geometric prequantization à la Kostant--Souriau.
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Loop Spaces, Characteristic Classes and Geometric Quantization (Paperback or Softback)
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Birkhauser 11/1/2007, 2007
ISBN 10: 0817647309
ISBN 13: 9780817647308
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Loop Spaces, Characteristic Classes and Geometric Quantization (Modern Birkhäuser Classics)
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Loop Spaces, Characteristic Classes and Geometric Quantization
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ISBN 13: 9780817647308
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. The book will be of interest to topologists, geometers, Lie theorists and mathematical physicists, as well as to operator algebraists. It is written for graduate students and researchers, and will be an excellent textbook. It has a self-contained introduction to the theory of sheaves and their cohomology, line bundles and geometric prequantization à la Kostant--Souriau. 320 pp. Englisch. Seller Inventory # 9780817647308
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Loop Spaces, Characteristic Classes and Geometric Quantization
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Loop Spaces, Characteristic Classes and Geometric Quantization
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Discusses open problems and further research extensionsWritten by a distinguished and well-published researcher in the fieldIncludes many examples and figuresThis book examines the differential geometry of manifolds, loop spa. Seller Inventory # 5975874
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. The book will be of interest to topologists, geometers, Lie theorists and mathematical physicists, as well as to operator algebraists. It is written for graduate students and researchers, and will be an excellent textbook. It has a self-contained introduction to the theory of sheaves and their cohomology, line bundles and geometric prequantization à la Kostant--Souriau. Seller Inventory # 9780817647308