Loop Spaces, Characteristic Classes and Geometric Quantization

Name: Loop Spaces, Characteristic Classes and Geometric Quantization
Brand: Springer, Basel
SKU: 9780817647308
Price: 406.92 RON
Availability: InStock

Autor: Jean-Luc Brylinski

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Legare: Carte broșată

Editura: Springer, Basel

Disponibilitate: În depozitul extern

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This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids...

Informații despre carte

Autor

Jean-Luc Brylinski

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2007

Pagini

302

EAN

9780817647308

ISBN

0817647309

Enbook ID

01399451

Editura

Springer, Basel

Greutate

454

Dimensiuni

156 x 234 x 17

Descriere completă

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

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Loop Spaces, Characteristic Classes and Geometric Quantization

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