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Loop Spaces, Characteristic Classes

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Birkhäuser, 1993 - Mathematics - 300 pages
This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Recent development in mathematical physics (e.g., in knot theory, gauge theory, and topological quantum filed theory) have led mathematicians and physicists to look 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 new 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, K'hler geometry of the space of knots, Cheeger-Cern-Simons secondary characteristics classes, and group cohomology. Finally, the last chapter deals with the Dirac monopole and Diraca's quantizations 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 prequantizations ? la Kostant-Souriau.

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Loop Spaces, Characteristic Classes and Geometric Quantization
Loop Spaces, Characteristic Classes and Geometric Quantization
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Loop Spaces, Characteristic Classes and Geometric Quantization
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Brylinski J.-L — Loop Spaces, Characteristic Classes and ...
Название: Loop Spaces, Characteristic Classes and Geometric Quantization Автор: Brylinski J.-L Аннотация:. Develops a Chern-Weil theory of characteristic ...
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Bibliographic information

QR code for Loop Spaces, Characteristic Classes
TitleLoop Spaces, Characteristic Classes
Volume 107 of Progress in Mathematics Series
AuthorJean-Luc Brylinski
Editionillustrated
PublisherBirkhäuser, 1993
ISBN0817636447, 9780817636449
Length300 pages
Subjects ›  › 

Mathematics / Algebra / General
Mathematics / General
Mathematics / Geometry / Differential
Mathematics / Topology
  
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