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OverviewThis book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Recent developments in mathematical physics (e.g., in knot theory, gauge theory and topological quantum field 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 fibre bundles (more precisely, associated to gerbes). The new theory is a 3-dimensional analogue 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, Kaehler geometry of the space of knots, Cheeger-Chern-Simons secondary characteristic 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 a la Kostant-Souriau. Full Product DetailsAuthor: Jean-Luc BrylinskiPublisher: Birkhauser Boston Inc Imprint: Birkhauser Boston Inc Edition: 1st ed. 1993. Corr. 2nd printing Volume: 107 Dimensions: Width: 15.50cm , Height: 2.00cm , Length: 23.50cm Weight: 0.632kg ISBN: 9780817636449ISBN 10: 0817636447 Pages: 318 Publication Date: 01 April 1994 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Out of Stock Indefinitely Availability: Out of stock Table of ContentsReviewsThe book is not only a well-written and thorough exposition of....abstract ideas, but it also treats geometric applications throughout... In addition, the book contains a nice exposition of various aspects of Cech, de Rham, and Deligne cohomology and an exposition of Grothendieck's decent theory for sheaves. <p>--Mathematical Reviews The book is not only a well-written and thorough exposition of...abstract ideas, but it also treats geometric applications throughout... In addition, the book contains a nice exposition of various aspects of Cech, de Rham, and Deligne cohomology and an exposition of Grothendieck's decent theory for sheaves. --Mathematical Reviews Author InformationTab Content 6Author Website:Countries AvailableAll regions |