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Catalogue Information
Field name	Details
Dewey Class	516.36
Title	Loop Spaces, Characteristic Classes and Geometric Quantization ([EBook]) / by Jean-Luc Brylinski.
Author	Brylinski, Jean-Luc
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Birkhäuser , 1993.
Physical Details	XVI, 302 pages : online resource.
Series	Progress in mathematics
ISBN	9780817647315
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-4731-5
Links to Related Works	Subject References: Algebra . Category Theory, Homological Algebra . Category theory (Mathematics) . Differential Geometry . Homological algebra . Mathematics . Topology . Authors: Brylinski, Jean-Luc . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 516.36 .

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Loop Spaces, Characteristic Classes and Geometric Quantization

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