Loop Spaces, Characteristic Classes and Geometric Quantization (Progress in Mathematics) - Jean-Luc Brylinski, Jean-Luc -L Brylinski (1994)
ISBN 0817636447
Subject Loop spaces; Characteristic classes; Homology theory
Publisher Birkhäuser Boston
Publication Date 4/1/1994
Format Hardcover (234 x 162 mm)
Language e

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, Kähler 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 Dirac’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 à la Kostant-Souriau.

Personal Details
Collection Status In Collection
Index 819
Read It Yes
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Product Details
LoC Classification QA612.76.B79 1993
Dewey 514/.24
Cover Price $89.95
No. of Pages 324