Loop Spaces, Characteristic Classes and Geometric Quantization: 107 (Progress in Mathematics) - Tapa dura

"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

This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. 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, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.