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Loop Spaces, Characteristic Classes and Geometric Quantization (Progress in Mathematics) by Jean-Luc Brylinski is a book available to read on EtoBox.

What is Loop Spaces, Characteristic Classes and Geometric Quantization (Progress in Mathematics) about?

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 theoris

Author

Jean-Luc Brylinski

Publisher

Birkhäuser Boston

Published

2009

Language

EN

ISBN

9780817636449

Subjects

Mathematics, Stem