Loop Spaces, Characteristic Classes and Geometric Quantization [electronic resource] /

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.

Bibliographic Details

Main Authors:	Brylinski, Jean-Luc. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 1993
Subjects:	Mathematics., Algebra., Category theory (Mathematics)., Homological algebra., Differential geometry., Topology., Differential Geometry., Category Theory, Homological Algebra.,
Online Access:	http://dx.doi.org/10.1007/978-0-8176-4731-5
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