Loop Spaces, Characteristic Classes and Geometric Quantization
(Sprache: Englisch)
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...
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Klappentext zu „Loop Spaces, Characteristic Classes and Geometric Quantization “
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.
Inhaltsverzeichnis zu „Loop Spaces, Characteristic Classes and Geometric Quantization “
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.
Bibliographische Angaben
- Autor: Jean-Luc Brylinski
- 2007, Reprint of the 1993 ed., 302 Seiten, 6 Abbildungen, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 0817647309
- ISBN-13: 9780817647308
- Erscheinungsdatum: 15.11.2007
Sprache:
Englisch
Rezension zu „Loop Spaces, Characteristic Classes and Geometric Quantization “
"The book is not only a well-written and thorough exposition of....abstract ideas, but it also treats geometric applications throughout... In addition, the book contains a nice exposition of various aspects of Cech, de Rham, and Deligne cohomology and an exposition of Grothendieck's decent theory for sheaves."
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