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＜電子ブック＞
Loop Spaces, Characteristic Classes and Geometric Quantization / by Jean-Luc Brylinski
(Modern Birkhäuser Classics. ISSN:21971811)

版	1st ed. 1993.
出版者	Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser
出版年	1993
本文言語	英語
大きさ	XVI, 302 p : online resource
冊子体	Loop spaces, characteristic classes and geometric quantization / Jean-Luc Brylinski ; : us,: sz
著者標目	*Brylinski, Jean-Luc author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Algebra LCSH:Topology LCSH:Algebra, Homological FREE:Differential Geometry FREE:Algebra FREE:Topology FREE:Category Theory, Homological Algebra
一般注記	Complexes of Sheaves and their Hypercohomology -- Line Bundles and Central Extensions -- Kähler Geometry of the Space of Knots -- Degree 3 Cohomology: The Dixmier-Douady Theory -- Degree 3 Cohomology: Sheaves of Groupoids -- Line Bundles over Loop Spaces -- The Dirac Monopole 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-0-8176-4731-5

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