Loop Spaces, Characteristic Classes and Geometric Quantization

Nachdruck of the 1993 Auflage 2007
ISBN: 978-0-8176-4730-8
Verlag: Birkhäuser Boston

Buch, Englisch, 302 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 487 g

Reihe: Modern Birkhäuser Classics

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. 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.

Zielgruppe

Research

Autoren/Hrsg.

Brylinski, Jean-Luc

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie

Inhaltsverzeichnis

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.