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Loop Spaces, Characteristic Classes and Geometric Quantization Jean-Luc Brylinski

Loop Spaces, Characteristic Classes and Geometric Quantization By Jean-Luc Brylinski

Loop Spaces, Characteristic Classes and Geometric Quantization by Jean-Luc Brylinski


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Summary

This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics.

Loop Spaces, Characteristic Classes and Geometric Quantization Summary

Loop Spaces, Characteristic Classes and Geometric Quantization by Jean-Luc Brylinski

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, Kahler 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.

Loop Spaces, Characteristic Classes and Geometric Quantization Reviews

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.

--Mathematical Reviews

Table of Contents

Complexes of Sheaves and their Hypercohomology.- Line Bundles and Central Extensions.- Kahler 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.

Additional information

NLS9780817647308
9780817647308
0817647309
Loop Spaces, Characteristic Classes and Geometric Quantization by Jean-Luc Brylinski
New
Paperback
Birkhauser Boston Inc
2007-11-15
302
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Loop Spaces, Characteristic Classes and Geometric Quantization